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This paper considers the problem of designing adaptive feedforward control (AFC) systems for uncertain single-input single-output linear systems perturbed by multisinusoidal disturbances of known frequencies. The proposed approach removes the longstanding assumption that either the sign of the real part or the imaginary part of the transfer function of a stable plant at the frequency of excitation is known for AFC to be applicable, which is referred to in this paper as a strictly positive real (SPR)-like condition. Notable features of the solution are that persistence of excitation is not required, and stability analysis tools based on averaging are avoided; hence, the requirement of an exponentially stable equilibrium for the closed-loop system is circumvented. [ABSTRACT FROM AUTHOR]

In this paper, we study attitude synchronization for elements in the unit sphere in $\mathbb {R}^{\scriptscriptstyle {\scriptscriptstyle {3}}}$ and for elements in the three-dimensional (3-D) rotation group, for a network with switching topology. The agents’ angular velocities are assumed to be the control inputs, and a switching control law for each agent is devised that guarantees synchronization, provided that all elements are initially contained in a region, which we identify later in the paper. The control law is decentralized and it does not require a common orientation frame among all agents. We refer to synchronization of unit vectors in $\mathbb {R}^{\scriptscriptstyle {3}}$ as incomplete synchronization, and of 3-D rotation matrices as complete synchronization. Our main contribution lies in showing that these two problems can be analyzed under a common framework, where all agents’ dynamics are transformed into unit vectors dynamics on a sphere of appropriate dimension. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a method to obtain necessary and sufficient stability conditions for systems governed by one-dimensional nonlinear hyperbolic partial-differential equations with closed-loop integral controllers, when the linear frequency analysis cannot be used anymore. We study the stability of a general nonlinear transport equation where the control input and the measured output are both located on the boundaries. The principle of the method is to extract the limiting part of the stability from the solution using a projector on a finite-dimensional space and then use a Lyapunov approach. This paper improves a result of Trinh, Andrieu, and Xu, and gives an optimal condition for the design of the controller. The results are illustrated with numerical simulations where the predicted stable and unstable regions can be clearly identified. [ABSTRACT FROM AUTHOR]

This paper proposes a less conservative stability criterion for discrete-time Lur'e systems with sector and slope restrictions by constructing a novel Lyapunov functional. Compared with the Lyapunov functional in the literature, this paper fully utilizes the sector and slope restrictions in our Lyapunov functional, which includes integral terms involved with the sector restriction of the nonlinearities $\phi (y_{i})$ and $\phi (y_{i+1})$ , integral terms involved with the slope restriction between $\phi (y_{i})$ and $\phi (y_{i+1})$ , and a quadratic term with an augmented vector related to available vectors for representing upper and lower bounds of all integral terms. The positive definiteness of a matrix appearing in the quadratic term can be relaxed by utilizing the lower bounds of all integral terms. Based on the Lyapunov functional, an improved stability criterion is derived in terms of linear matrix inequalities. Numerical examples show the effectiveness of the proposed criterion. [ABSTRACT FROM AUTHOR]

This paper deals with the estimation of convergence rate and domain of attraction of control-Lyapunov functions in Lyapunov-based control. This pair of estimation problems has been considered only for input-affine systems with constraints on the input norm. In this paper, we propose a novel optimization framework to address the estimation of convergence rate and domain of attraction. Specifically, we formulate the estimation problems as min–max bilevel programs for the decay rate of the Lyapunov function, where the inner problem can be resolved using Karush–Kuhn–Tucker optimality conditions, and the resulting single-level programs can be transformed into and solved as mixed-integer nonlinear programs. The proposed approach is applicable to systems with input-nonaffinity or more general forms of input constraints under an input-convexity assumption. [ABSTRACT FROM AUTHOR]

In this article, we first show that the main results claimed in the paper by Bikas and Rovithakis (2021) involve some errors as the selection conditions for the design parameters are not sufficient to ensure the boundedness of all the closed-loop signals, then we provide the corresponding corrections under the same controller, so that the underlying quantized control problem can be tackled. [ABSTRACT FROM AUTHOR]

A popular design framework for networked control systems (NCSs) is the emulation-based approach combined with Lyapunov-based analysis techniques for hybrid systems. In virtually all papers that use this framework, bounds in terms of the maximal allowable transmission interval (MATI) are provided to guarantee stability, and performance properties of the NCS. However, having only such a MATI condition is rather restrictive, and unrealistic in practice due to various network effects such as packet losses, leading to conservative bounds. In this article, we therefore consider an alternative condition on the communication instants to better capture the time-varying properties of the transmission intervals. In particular, we propose, in addition to the existence of a MATI, to also impose a bound on the average allowable transmission interval, expressed in terms of a reverse average dwell-time condition on the transmission intervals. We demonstrate by means of a novel Lyapunov-based analysis that stability of the NCS can still be guaranteed under this different condition on the transmission intervals, which can, in addition, lead to a significant improvement of the MATI. The strengths of these new results will be illustrated on a numerical example. [ABSTRACT FROM AUTHOR]

In this paper, tools to study forward invariance properties with robustness to disturbances, referred to as robust forward invariance, are proposed for hybrid dynamical systems modeled as hybrid inclusions. Hybrid inclusions are given in terms of differential and difference inclusions with state and disturbance constraints, for whose definition only four objects are required. The proposed robust forward invariance notions allow for the diverse type of solutions to such systems (with and without disturbances), including solutions that have persistent flows and jumps, that are Zeno, and that stop to exist after finite amount of (hybrid) time. Sufficient conditions for sets to enjoy such properties are presented. These conditions are given in terms of the objects defining the hybrid inclusions and the set to be rendered robust forward invariant. In addition, as special cases, these conditions are exploited to state results on nominal forward invariance for hybrid systems without disturbances. Furthermore, results that provide conditions to render the sublevel sets of Lyapunov-like functions forward invariant are established. Analysis of a controlled inverter system is presented as an application of our results. Academic examples are given throughout this paper to illustrate the main ideas. [ABSTRACT FROM AUTHOR]

This paper deals with the certification problem for robust quadratic stability, robust state convergence, and robust quadratic performance of linear systems that exhibit bounded rates of variation in their parameters. We consider both continuous-time (CT) and discrete-time (DT) parameter-varying systems. In this paper, we provide a uniform method for this certification problem in both cases and we show that, contrary to what was claimed previously, the DT case requires a significantly different treatment compared to the existing CT results. In the established uniform approach, quadratic Lyapunov functions, which are affine in the parameter, are used to certify robust stability, robust convergence rates, and robust performance in terms of linear matrix inequality feasibility tests. To exemplify the procedure, we solve the certification problem for $\mathscr {L}_2$ -gain performance both in the CT and the DT cases. A numerical example is given to show that the proposed approach is less conservative than a method with slack variables. [ABSTRACT FROM AUTHOR]

This article investigates adaptive state-feedback stabilization problem for a class of stochastic high-order nonlinear systems with unknown time-varying powers and stochastic inverse dynamics for the first time. The existence of stochastic inverse dynamics, unknown parameters, and time-varying powers makes stochastic high-order nonlinear systems essentially different from the related papers, which brings a series of obstacles to achieve the control objective. By virtue of the parameter separation principle, adaptive technique and some flexible algebraic methods, a novel adaptive state-feedback controller is designed to guarantee that the equilibrium of the closed-loop system is globally stable in probability. Finally, a simulation is provided to demonstrate the effectiveness of the control scheme. [ABSTRACT FROM AUTHOR]

This paper addresses the problems of determining the \mathcal H_2 norm and the root mean square (RMS) gain of continuous-time switched linear systems. A novel class of Lyapunov functions is proposed for reaching this goal, called homogeneous rational Lyapunov functions (HRLFs). It is shown that sufficient conditions for establishing upper bounds of the sought performance indexes in the case of arbitrary switching can be given in terms of linear matrix inequality (LMI) feasibility tests by searching for an HRLF of chosen degree. Moreover, it is shown that these conditions are also necessary by searching for an HRLF of degree sufficiently large. It is worth mentioning that necessary and sufficient LMI conditions have not been proposed yet in the literature for the considered problems. Hence, the paper continues by considering the case of switching with dwell time constraints, showing that analogous LMI conditions can be obtained for this case by searching for a family of HRLFs mutually constrained by the dwell time specification. Some numerical examples illustrate the proposed methodology and highlight the advantages with respect to the existing works. [ABSTRACT FROM AUTHOR]

This paper considers a standard consensus algorithm under output saturations. In this case, the global consensus cannot be realized due to the existence of stable equilibrium points that do not belong to the consensus manifold. Therefore, this paper investigates necessary and sufficient initial conditions for the achievement of consensus that characterize an exact domain of attraction. Specifically, this paper considers single-integrator agents with both fixed and time-varying undirected graphs. Then, we show that the consensus will be achieved if and only if the average of the initial states is within the minimum saturation level. [ABSTRACT FROM AUTHOR]

In this paper, we analyse convergence and stability properties for piecewise affine models of gene regulatory networks, by means of piecewise quadratic Lyapunov functions. In the first part, we present the piecewise affine model of a gene regulatory network then, after proving a result on the existence of a minimal, attractive, and positively invariant box, we describe a linear matrix inequalitie framework to construct a Lyapunov function for the system. In the second part of the work, after a characterization of the system solutions when considering also isolated Zeno behavior of the trajectories, a monotonicity property of the so found Lyapunov function is formally proved, together with a result on the convergence of the trajectories, in the sense of measure. Finally, we present two examples, showing the applicability and utility of the main theoretical results previously explained. [ABSTRACT FROM AUTHOR]

In this paper, two control schemes producing a continuous control signal are presented for a perturbed triple integrator: The continuous twisting algorithm (3-CTA) and the output feedback continuous twisting algorithm (3-OFCTA). The first one is a state feedback controller that ensures global finite-time stability of the origin, despite of Lipschitz, nonvanishing, and matched disturbances. It provides steady-state precision of fourth order of the output w.r.t. sampling step. The second one is an output feedback controller, which uses a third-order robust and exact differentiator as an observer. By requiring only information of the measurable output, the 3-OFCTA preserves all features of robustness, convergence, and precision of the state feedback 3-CTA. Moreover, it is proven that a separation principle applies, so that the gains of the controller and of the observer can be selected independently to assure stability. [ABSTRACT FROM AUTHOR]

Persistently excited nonlinear time-varying systems are considered in this paper. Two new quadratic, time-varying, Lyapunov functions are presented, whose time-varying matrices—solutions to suitable linear time-varying matrix differential equations—are causal (nonanticipating) and, thus, differently from related results in the literature, available at runtime. They allow for directly addressing and successfully achieving further adaptation goals, when uncertain parameters affect the system dynamics. [ABSTRACT FROM AUTHOR]

This paper employs detectability ideas to decide uniform global asymptotic stability (UGAS) of the trivial solution for a class of switched nonlinear time-varying systems when the trivial solution is uniformly globally stable. Using the notion of limiting behaviors of the state, output, and switching signals, the concept of a limiting zeroing-output solution is introduced. This leads to a definition of weak zero-state detectability (WZSD) that can be used to check UGAS, (uniformly for a set of switched signals). En route to establish this, a number of new stability results are derived. For example, under appropriate conditions, it is feasible to decide UGAS even when the switching signal does not satisfy an averaged dwell-time condition. It is also shown that WZSD of the original switched system can be verified by detectability conditions of much simpler auxiliary systems. Moreover, UGAS can be guaranteed without requiring that in each allowable system (without switching), the trivial solution is attractive. The effectiveness of the proposed concept is illustrated by a few examples including a switched semi-quasi-Z-source inverter. [ABSTRACT FROM AUTHOR]

It is proved in this paper that the existence of a delay-dependent suitable Lyapunov function is a necessary and sufficient condition for a discrete-time fully nonlinear time-delay system, with given delays digraph, to be globally asymptotically stable. The same result is provided for the input-to-state stability. The less is the number of edges in the delays digraph, the less is the number of inequalities that are involved in the provided necessary and sufficient Lyapunov conditions. The case of arbitrary time-varying time delays, with no constraints as long as bounded, is covered as a special case. [ABSTRACT FROM AUTHOR]

In this paper, we present a method to robustify asymptotically stable nonlinear systems by adding an integral action that rejects unknown additive disturbances. The proposed approach uses a port-Hamiltonian (pH) representation of the open-loop dynamics, which, relying on the asymptotic stability property, is guaranteed to exist. The integral action controller preserves the pH structure, and, by adding a suitable cross term between the plant and the controller states to the closed-loop energy function, it avoids the unnatural coordinate transformation used in the past. The controller is shown to be robust against some common types of modeling uncertainty, including unknown friction dynamics in mechanical systems. [ABSTRACT FROM AUTHOR]

In this paper, we study connections between structured storage or Lyapunov functions of a class of interconnected systems (dynamical networks) and dissipativity properties of the individual systems. We prove that if a dynamical network, composed as a set of linear time invariant systems interconnected over an acyclic graph, admits an additive quadratic Lyapunov function, then the individual systems in the network are dissipative with respect to a (nonempty) set of interconnection neutral supply functions. Each supply function from this set is defined on a single interconnection link in the network. Specific characterizations of neutral supply functions are presented, which imply robustness of network stability/dissipativity to removal of interconnection links. [ABSTRACT FROM AUTHOR]

Periodic event-triggered control (PETC) is an appealing paradigm for the implementation of controllers on platforms with limited communication resources, a typical example being networked control systems. In PETC, transmissions over the communication channel are triggered by an event generator, which depends solely on the available plant and controller data and is only evaluated at given sampling instants to enable its digital implementation. In this paper, we consider the general scenario, where the controller communicates with the plant via multiple decoupled networks. Each network may contain multiple nodes, in which case a dedicated protocol is used to schedule transmissions among these nodes. The transmission instants over the networks are asynchronous and generated by local event generators. At given sampling instants, the local event generator evaluates a rule, which only involves the measurements and the control inputs available locally, to decide whether a transmission is needed over the considered network. Following the emulation approach, we show how to design local triggering generators to ensure input-to-state stability and $\mathcal {L}_p$ stability for the overall system based on a continuous-time output-feedback controller that robustly stabilizes the network-free system. The method is applied to a class of Lipschitz nonlinear systems, for which we formulate the design conditions as linear matrix inequalities. The effectiveness of the scheme is illustrated via simulations of a nonlinear example. [ABSTRACT FROM AUTHOR]

A constructive tool of nonlinear control system design, the method of control Lyapunov functions (CLFs), has found numerous applications in stabilization problems for continuous-time, discrete-time, and hybrid systems. In this paper, we address the fundamental question: Given a CLF, corresponding to a continuous-time controller with some predefined (e.g., exponential) convergence rate, can the same convergence rate be provided by an event-triggered controller? Under certain assumptions, we give an affirmative answer to this question and show that the corresponding event-based controllers provide positive dwell times between consecutive events. Furthermore, we prove the existence of self-triggered and periodic event-triggered controllers, providing stabilization with a known convergence rate. [ABSTRACT FROM AUTHOR]

We prove that if a homogeneous, continuously differentiable vector field is asymptotically stable, then it admits a Lyapunov function, which is the ratio of two polynomials (i.e., a rational function). We further show that when the vector field is polynomial, the Lyapunov inequalities on both the rational function and its derivative have sum of squares certificates and, hence, such a Lyapunov function can always be found by semidefinite programming. This generalizes the classical fact that an asymptotically stable linear system admits a quadratic Lyapunov function, which satisfies a certain linear matrix inequality. In addition to homogeneous vector fields, the result can be useful for showing local asymptotic stability of nonhomogeneous systems by proving asymptotic stability of their lowest order homogeneous component. This paper also includes some negative results: We show that in absence of homogeneity, globally asymptotically stable polynomial vector fields may fail to admit a global rational Lyapunov function, and in presence of homogeneity, the degree of the numerator of a rational Lyapunov function may need to be arbitrarily high (even for vector fields of fixed degree and dimension). On the other hand, we also give a family of homogeneous polynomial vector fields that admit a low-degree rational Lyapunov function but necessitate polynomial Lyapunov functions of arbitrarily high degree. This shows the potential benefits of working with rational Lyapunov functions, particularly as the ones whose existence we guarantee have structured denominators and are not more expensive to search for than polynomial ones. [ABSTRACT FROM AUTHOR]

The explicit reference governor (ERG) is a simple and systematic approach that provides constraint handling capabilities to prestabilized systems. The basic idea behind this approach is to translate state and input constraints into an upper-bound on the value of the Lyapunov function, which is then enforced by suitably manipulating the derivative of the applied reference. When designing the ERG, one of the main challenges is the determination of an upper-bound on the value of the Lyapunov function that ensures constraints satisfaction. This paper proposes a systematic approach for estimating online the optimal upper-bound for systems subject to the intersection of concave constraints. To do this, the Barrier function method is used. The effect of the estimation error caused by the time-varying nature of the auxiliary reference on the constraint satisfaction capability of the ERG is studied analytically. A procedure is proposed to modify the estimated upper-bound to avoid constraints violation in the presence of estimation errors. The effectiveness of the proposed scheme is demonstrated through a simulation study on an overhead gantry crane system. [ABSTRACT FROM AUTHOR]

In this paper, input-to-state stability (ISS) for discrete-time switched nonlinear time-varying (SNTV) systems is investigated. Starting with discrete-time nonlinear time-varying (NTV) systems, some improved sufficient conditions are proposed to verify the ISS of systems by using the weak implication-form ISS (WI-ISS) Lyapunov function, weak dissipative-form ISS (WD-ISS) Lyapunov function, and interval descent technique. Then, the results obtained are extended to study the ISS of discrete-time SNTV systems, several relaxed conditions are given by using piecewise WI-ISS and WD-ISS Lyapunov functions, minimum dwell time, and infinite switching methods, respectively. Comparing with the existing results, the obtained conditions release the requirement on negative definiteness of the differences of (piecewise) Lyapunov functions, moreover, all subsystems are allowed to be unstable in the case of infinite switching. Finally, a numerical example is given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

The joint spectral radius (JSR) of a set of matrices characterizes the maximal asymptotic growth rate of an infinite product of matrices of the set. This quantity appears in a number of applications including the stability of switched and hybrid systems. A popular method used for the stability analysis of these systems searches for a Lyapunov function with convex optimization tools. We analyze the accuracy of this method for constrained switched systems, a class of systems that has attracted increasing attention recently. We provide a new guarantee for the upper bound provided by the sum of squares implementation of the method. This guarantee relies on the $p$ -radius of the system and the entropy of the language of allowed switching sequences. We end this paper with a method to reduce the computation of the JSR of low-rank matrices to the computation of the constrained JSR of matrices of small dimension. [ABSTRACT FROM AUTHOR]

The paper deals with stabilization of feedforward multiple cascade dynamics under sampling. It is shown that u-average passivity concepts and Lyapunov methods can be profitably exploited to provide a systematic sampled-data design procedure. The proposed methodology recalls the continuous-time feedforwarding steps and can be applied under the same assumptions as those set over the continuous-time cascade dynamics. The final sampled feedback is carried out through a three-steps procedure that involves iterative passivation and stabilization in the u-average sense. Constructive aspects are developed to compute approximate solutions which are indeed implemented in practice. An example is worked out with comparative simulations with respect to usual sampled-and-hold implementations. [ABSTRACT FROM AUTHOR]

An essential problem in the coordination of multiple agents is formation control. Significant challenges to the theoretical design may arise when the multiagent system is subject to uncertainty. This paper considers the robust multitask formation control problem for multiple agents, whose communication and measurements are disturbed by uncertain parameters. The control objectives include achieving the desired configuration, avoiding collisions, and preserving the connectivity of the uncertain topology. To achieve these objectives, we first provide conditions in terms of linear matrix inequalities for checking the connectivity of uncertain topologies. Then, we propose a new type of Lyapunov-like barrier function, called parametric Lyapunov-like barrier function, that is applicable to multiagent systems with uncertainties in communication and measurements. It is shown that this new type of Lyapunov-like barrier function guarantees the robust multitask formation and displays advantages over parameter-independent Lyapunov-like barrier functions. The efficacy of the proposed method is demonstrated via simulation results. [ABSTRACT FROM AUTHOR]

This paper studies input-to-state stability for hybrid systems with memory, which models hybrid dynamics affected by time delays. Using both Lyapunov–Razumikhin functions and Lyapunov–Krasovskii functionals, Lyapunov-based sufficient conditions are established for input-to-state stability. In addition, further extensions and relaxations are proposed for special cases, such as the stable flow/jump cases and the cases that Lyapunov functions do not decrease strictly during flow/jumps. Finally, two examples are used to illustrate the developed results [ABSTRACT FROM AUTHOR]

In this paper, the stability and $L_2$ -gain properties of linear impulsive delay systems with delayed impulses are studied. Commonly employed techniques, in which the delayed impulses are treated using Newton–Leibniz formula, may not be applicable to $L_2$ -gain analysis, since they make the disturbance input appear in the impulse part. In order to circumvent the difficulty, we first augment the considered system to a time-delay system with switching nondelayed impulses. Due to the absence of delayed impulses, this new approach has advantages in constructing Lyapunov functions and handling the effects of impulse delays on the system performance. Switching-based time-dependent Lyapunov functions are introduced to deal with the resultant switching impulses of the augmented system. Sufficient conditions for exponential stability and $L_2$ -gain properties are derived in terms of linear matrix inequalities. Numerical examples are provided to illustrate the efficiency of the new approach. [ABSTRACT FROM AUTHOR]

This paper studies the stability for impulsive switched time-delay systems with state-dependent impulses. Since the impulses and the switches are not necessarily synchronous, we start from a stability analysis of impulsive switched time-delay systems with time-dependent impulses. Sufficient conditions are derived to guarantee the stability property, which extends the previous results for the synchronous switch and impulse case. For the state-dependent impulse case, using the B-equivalent method, impulsive switched time-delay systems with state-dependent impulses are transformed into impulsive switched time-delay systems with time-dependent impulses. The equivalence between the original system and the transformed system is established, and stability conditions are obtained for impulsive switched time-delay systems with state-dependent impulses. Finally, a numerical example is given to demonstrate the obtained results. [ABSTRACT FROM AUTHOR]

Previous small-gain results for interconnected integral input-to-state (iISS) systems have been restricted to systems that are strongly iISS. This paper removes this restriction by allowing cross terms between external inputs and states in the Lyapunov decrease of component systems, and subsequently constructing a nonseparable Lyapunov function. An example demonstrates the use of this new small-gain formulation. [ABSTRACT FROM AUTHOR]

When sum-of-squares (SOS) programs are recast as semidefinite programs (SDPs) using the standard monomial basis, the constraint matrices in the SDP possess a structural property that we call partial orthogonality. In this paper, we leverage partial orthogonality to develop a fast first-order method, based on the alternating direction method of multipliers (ADMM), for the solution of the homogeneous self-dual embedding of SDPs describing SOS programs. Precisely, we show how a “diagonal plus low rank” structure implied by partial orthogonality can be exploited to project efficiently the iterates of a recent ADMM algorithm for generic conic programs onto the set defined by the affine constraints of the SDP. The resulting algorithm, implemented as a new package in the solver CDCS, is tested on a range of large-scale SOS programs arising from constrained polynomial optimization problems and from Lyapunov stability analysis of polynomial dynamical systems. These numerical experiments demonstrate the effectiveness of our approach compared to common state-of-the-art solvers. [ABSTRACT FROM AUTHOR]

In this paper, the stability, stabilization, and $L_{2}$ -gain problems are investigated for periodic piecewise systems with time-varying subsystems. Continuous Lyapunov function with time-varying Lyapunov matrix is adopted. A condition guaranteeing the negative definiteness of a matrix polynomial, deriving from the Lyapunov derivative, is first obtained. Based on such a condition, an exponential stability condition is provided. Moreover, a state-feedback controller with time-varying gain is developed to stabilize the unstable periodic piecewise time-varying system. The $L_{2}$ -gain criterion for periodic piecewise time-varying system is also studied. Numerical examples are given to show the validity of the proposed techniques. [ABSTRACT FROM AUTHOR]

In this paper, we consider a multi-input driftless bilinear system evolving on the $n$ -dimensional sphere $S^{n}$. We first provide examples drawn from rigid body mechanics that provide the motivation for the control of bilinear systems on $S^{n}$. For the general framework, we establish the global controllability on $S^{n}$ and propose two linear control laws on $S^{n}$ that achieve asymptotic stabilization of an equilibrium point with an almost global domain-of-attraction. Further, the asymptotically stable closed-loop system trajectories are shown to be arcs on the geodesics of $S^{n}$ for a particular choice of the equilibrium point. Next, we propose two linear time-varying control laws to achieve trajectory tracking on $S^{n}$ and show the asymptotic stability of the tracking error. A distributed control is designed for the consensus of multiagent bilinear systems on $S^{n}$ with an undirected tree as the communication graph. The consensus manifold is shown to have an almost global domain of attraction. [ABSTRACT FROM AUTHOR]

In this paper, the effects of bounded disturbances on decentralized event-triggered control systems are studied. The input-to-state (practical) stability of integral-based event-triggered control systems and dynamic event-triggered control systems is analyzed in a uniform framework by utilizing a new Lyapunov functional approach. An estimation on the upper bound of the input-to-state stability gain is given analytically. First, Zeno behavior is excluded with the time-regularized mechanisms, that is, a prespecified lower bound of inter-event times is introduced. Then, the conditions are presented under which the considered event-triggered control systems ensure Zeno-freeness without time regularization. Finally, a numerical example is given to illustrate the efficiency and feasibility of the proposed results. [ABSTRACT FROM AUTHOR]

In this paper we study the stability of nonlinear and time-varying switched systems under restricted switching. We approach the problem by decomposing the system dynamics into a nominal-like part and a perturbation-like one. Most stability results for perturbed systems are based on the use of strong Lyapunov functions, i.e. functions of time and state whose total time derivative along the nominal system trajectories is bounded by a negative definite function of the state. However, switched systems under restricted switching may not admit strong Lyapunov functions, even when asymptotic stability is uniform over the set of switching signals considered. The main contribution of the current paper consists in providing stability results that are based on the stability of the nominal-like part of the system and require only a weak Lyapunov function. These results may have wider applicability than results based on strong Lyapunov functions. The results provided follow two lines. First, we give very general global uniform asymptotic stability results under reasonable boundedness conditions on the functions that define the dynamics of the nominal-like and the perturbation-like parts of the system. Second, we provide input-to-state stability (ISS) results for the case when the nominal-like part is switched linear-time-varying. We provide two types of ISS results: standard ISS that involves the essential supremum norm of the input and a modified ISS that involves a power-type norm. [ABSTRACT FROM AUTHOR]

This paper investigates standard $H_\infty$ control of switched systems via dwell-time switchings without posing any internal stability requirements on subsystems of the switched systems. First, a sufficient condition is formed by specifying lower and upper bounds of the dwell time, constraining upper bound of derivative of a Lyapunov function of the active subsystem, and forcing the Lyapunov function values of the overall switched system to decrease at switching times to achieve standard $H_\infty$ control of unforced switched linear systems. Then, in the same framework of the dwell time, sufficient conditions are given for that of the corresponding forced switched linear systems by further designing state feedback controllers. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the study of both, local and global, uniform asymptotic stability for switched nonlinear time-varying (NLTV) systems through the detectability of output-maps. With this aim, the notion of reduced limiting control systems for switched NLTV systems whose switchings verify time/state-dependent constraints, and the concept of weak zero-state detectability for those reduced limiting systems are introduced. Necessary and sufficient conditions for the (global)uniform asymptotic stability of families of trajectories of the switched system are obtained in terms of this detectability property. These sufficient conditions in conjunction with the existence of multiple weak Lyapunov functions yield a criterion for the (global) uniform asymptotic stability of families of trajectories of the switched system. This criterion can be seen as an extension of the classical Krasovskii-LaSalle theorem. An interesting feature of the results is that no dwell-time assumptions are made. Moreover, they can be used for establishing the global uniform asymptotic stability of the switched NLTV system under arbitrary switchings. The effectiveness of the proposed results is illustrated by means of various interesting examples, including the stability analysis of a semiquasi-Z-source inverter [ABSTRACT FROM AUTHOR]

Compositional control methods are well-suited for the design of large-scale control systems. QSR-dissipativity and passivity are closely related to stability and may be utilized to show Lyapunov and finite-gain stability for dynamical systems under certain conditions. Additionally, passivity is preserved under feedback and parallel interconnections of passive systems and may be utilized to build larger stable systems. In this paper, we present a QSR-dissipativity and passivity based analysis for event-triggered networked control systems (NCSs). We characterize QSR-dissipativity, passivity, and stability conditions for an event-triggered NCS in cases where an input–output event-triggering sampler is located on the plant's side, controller's side, or both sides leading to a considerable decrease in the communication load among subunits. We calculate passivity levels for the entire NCS. We show that the general passivity and stability conditions of the NCS depend on passivity properties of the plant and controller. Our results illustrate the tradeoffs amongst passivity levels, stability, and the rates of communication between subsystems. The motivation behind our work is that by designing and connecting individual stable passive event-triggered NCSs with desired passivity levels, one can design larger stable passive compositional networked systems that are suitable for the design and control of large-scale systems, such as cyber-physical systems. [ABSTRACT FROM AUTHOR]

Although the finite-time control theory and application have been studied very well in the literature, few results are concerned with the effect of sampled-data control. In this paper, first, the stability analysis of a chain of integrators under a discretized finite-time controller is given. Then, in the presence of disturbance, the robustness of the closed-loop system is also investigated. Based on a Lyapunov method, the ultimate bound for the steady states of the considered closed-loop system is estimated. Some simulation and examples are provided to verify the proposed theoretical results. [ABSTRACT FROM AUTHOR]

It is proved in this paper that the existence of suitable multiple Lyapunov functions is a necessary and sufficient condition for a discrete-time nonlinear switching system, with given switches digraph, to be globally asymptotically stable. The same result is provided for the input-to-state stability. The less is the number of edges in the switches digraph, the less is the number of inequalities that are involved in the provided necessary and sufficient Lyapunov conditions. [ABSTRACT FROM AUTHOR]

This paper considers the input-to-state stability (ISS) of time-varying switched systems with time delays, where the upper bound estimation for the operator of Lyapunov function (UBEOL) is assumed to be time varying and mode dependent. The ISS and integral ISS are investigated for time-varying switched systems with time delays by using the Lyapunov–Razumikhin and comparison theorem methods. Since the coefficient in the UBEOL is time varying and takes a positive/negative value, the subsystems consist of both ISS and non-ISS subsystems, simultaneously. It is shown that our presented results have wider applications than some existing works. Two examples, including one of the consensus for time-varying multiagent systems with cooperative and competitive protocols, are presented to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

The goal of this paper is to design a stabilizing feedback boundary control for a reaction–diffusion partial differential equation (PDE), where the boundary control is subject to a constant delay while the equation may be unstable without any control. For this system, which is equivalent to a parabolic equation coupled with a transport equation, a prediction-based control is explicitly computed by splitting the infinite-dimensional system into two parts: a finite-dimensional unstable part and a stable infinite-dimensional part. A finite-dimensional delayed controller is computed for the unstable part, and it is shown that this controller stabilizes the whole PDE. The proof is based on an explicit expression of the classical Artstein transformation combined with an adequately designed Lyapunov function. A numerical simulation illustrates the constructive feedback design method. [ABSTRACT FROM AUTHOR]

Stability analysis of nonlinear singular systems, arising from differential algebraic equations, is addressed in this paper, exploiting the fact that it belongs to the class of Positvstellensatz problems. By means of the direct Lyapunov method and a variety of convex descriptor forms, sufficient conditions in terms of linear matrix inequalities are developed. Issues concerning proper initialization and simulation are also considered. Illustrative examples are provided. [ABSTRACT FROM AUTHOR]

Equilibrium-independent dissipativity (EID) is a recently introduced system property that requires a system to be dissipative with respect to any forced equilibrium configuration. This paper is a detailed examination of EID with quadratic supply rates for a common class of nonlinear control-affine systems. We provide an algebraic characterization of EID for such systems in the spirit of the Hill–Moylan lemma, where the usual stability condition is replaced by an incremental stability condition. Based on this characterization, we state results concerning internal stability, feedback stability, and absolute stability of EID systems. Finally, we study EID for discrete-time systems, providing the relevant definitions and an analogous Hill–Moylan-type characterization. Results for both continuous-time and discrete-time systems are illustrated through examples on physical systems and convex optimization algorithms. [ABSTRACT FROM AUTHOR]

This paper considers the stability analysis of nonlinear Lurie type systems where the nonlinearity is both (locally) sector and slope restricted. Convex conditions for verifying stability, computing outer estimates of reachable sets, and upper bounds on the induced $\mathcal {L}_2$ gain in a local or global domain are proposed. The conditions use a Lyapunov function that is quadratic on both the states and the nonlinearity and has an integral term on the nonlinearity. Numerical examples outline the benefits of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper is concerned with the regional stabilization problem for discrete time-delay systems with actuator saturations. Different from some existing delay-independent techniques handling the saturation nonlinearity, a delay-dependent polytopic approach is first proposed in a discrete-time framework. Then, by combining with an augmented Lyapunov function, a discrete Wirtinger-based inequality and some novel analysis techniques, improved delay-dependent regional stabilization conditions are established by means of linear matrix inequalities. Finally, it is shown via two numerical examples that the obtained results are less conservative than some existing ones yet providing a larger estimate of an initial condition set. [ABSTRACT FROM AUTHOR]

This paper presents a small-gain result for large-scale interconnected systems composed of hybrid subsystems. It is assumed that the subsystems are input-to-output practically stable (IOpS) with offset and unboundedness observability (UO), and the interconnected system can be proved to be IOpS with offset and UO as long as the proposed small-gain condition is satisfied. If, moreover, the assumption of IOpS on the subsystems is reduced to input-to-output stability (IOS), then the interconnected system is IOS. [ABSTRACT FROM AUTHOR]

This paper generalizes the LaSalle–Yoshizawa Theorem to switched nonsmooth systems. The Filippov and Krasovskii regularizations of a switched system are shown to be contained within the convex hull of the Filippov and Krasovskii regularizations of the subsystems, respectively. A common candidate Lyapunov function that has a negative semidefinite generalized time derivative along the trajectories of the subsystems is shown to be sufficient to establish LaSalle–Yoshizawa-like results for the switched system. Of independent interest, are the results on approximate continuity and Filippov regularization of set-valued maps, reduction of differential inclusions using Lipschitz continuous regular functions, and comparative remarks on different generalizations of the time derivative along the trajectories of a nonsmooth system. [ABSTRACT FROM AUTHOR]

In this paper, the input-to-state stability is studied for stochastic impulsive switched time-delay systems. Using the vector Lyapunov function, average dwell time, and the properties of $M$ -matrix, different types of sufficient conditions are established. Both the case that the continuous dynamics is stable and the case that the discrete dynamics is stable are addressed, and the stability conditions are obtained. In the obtained stability conditions, different components of the vector Lyapunov function are allowed to be coupled; the information in consecutive impulsive switching intervals is also allowed to be coupled. Therefore, the magnification on the corresponding coupling items is avoided and the obtained results are more general and less conservative than the existing results. Furthermore, we investigate the relationships among the vector Lyapunov function approach, the approach based on the comparison principle and the scalar Lyapunov function approach. According to the vector Lyapunov function, the comparison system is constructed and the scalar-Lyapunov-function-based stability conditions are established. Finally, the applicability of our results is illustrated through two examples from neural systems and the synchronization problem of chaos-based secure communication systems. [ABSTRACT FROM AUTHOR]