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Aiming at a class of switched uncertain nonlinear strict-feedback systems under the action of average dwell time switching signal, this paper proposes a novel adaptive neural network output feedback tracking control based on the consideration of the full state constraints. The controller is proposed based on neural networks. One of the key characteristics of the system discussed is that the state variables cannot be measured and the system states need to be kept within the constraint ranges. For the sake of estimating the unmeasured states, the observer is constructed. In order to ensure all states which are within the time-varying boundary, the tangent barrier Lyapunov function (BLF-Tan) is selected in the design process. The boundedness of the closed-loop signals with average dwell time is guaranteed by the designed controllers and all the states limit in their constrained sets. It has been proved that the output tracking error converge to a small neighborhood of zero. In addition, the significance of the presented control strategy is verified and tested by a simulation example. [ABSTRACT FROM AUTHOR]

This paper addresses the stability issue of a class of delayed switched cascade nonlinear systems consisting of separate subsystems and coupling terms between them. Some global and local asymptotic stability sufficient conditions are proposed, drawing stability conclusion of the overall cascade system from those of separate systems. These results essentially rely on the following observation: For a general delayed switched nonlinear system being asymptotically stable, the trajectories of the perturbed system asymptotically approach zero if so does the perturbation. This observation is one of the main results in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we propose new algebraic Gramians for continuous-time switched linear systems, which satisfy generalized Lyapunov equations. The main contribution of this paper is twofold. First, we show that the ranges of those Gramians encode the reachability and observability spaces of a switched linear system. As a consequence, a simple Gramian-based criterion for reachability and observability is established. Second, a balancing-based model order reduction technique is proposed and, under some sufficient conditions, stability preservation and an error bound are shown. Finally, the efficiency of the proposed method is illustrated by means of numerical examples. [ABSTRACT FROM AUTHOR]

This paper studies stability of stochastic impulsive switched systems. Different from exponential Lyapunov function and average dwell-time in the previous works, general Lyapunov function and fixed dwell-time are implemented in this paper to analyze input-to-state stability and global stability of stochastic impulsive switched systems. Two cases are investigated, that is, the case that the continuous dynamics is stable and the case that the discrete dynamics is stable. To implement multiple Lyapunov functions, there are two subcases considered in this paper: the subcase that the estimates on the derivatives of the multiple Lyapunov functions are the same and the subcase that the growths of the multiple Lyapunov functions by the jumps are the same. For aforementioned different cases, sufficient stability conditions are established for stochastic impulsive switched systems. Finally, the developed theory is illustrated through examples from networked control systems and synchronization problem of 3-D novel chaotic circuit systems. [ABSTRACT FROM PUBLISHER]

This paper solves the finite-time switching control issue for the nonstrict-feedback nonlinear switched systems. The controlled plants contain immeasurable states, arbitrarily switchings, and the unknown functions which are constructed with the whole states. Neural network is used to simulate the uncertain systems and a filter-based state observer is designed to estimate the immeasurable states in this paper, respectively. Based on the backstepping recursive technique and the common Lyapunov function method, a finite-time switching control method is presented. Due to the developed finite-time control strategy, the closed-loop signals can be ensured to be bounded under arbitrarily switchings, and the outputs of systems can quickly track the desired reference signals in finite time. The effectiveness of the proposed method is given through its application to a mass-spring-damper system. [ABSTRACT FROM AUTHOR]

In this paper, the problem of adaptive neural state-feedback tracking control is considered for a class of stochastic nonstrict-feedback nonlinear switched systems with completely unknown nonlinearities. In the design procedure, the universal approximation capability of radial basis function neural networks is used for identifying the unknown compounded nonlinear functions, and a variable separation technique is employed to overcome the design difficulty caused by the nonstrict-feedback structure. The most outstanding novelty of this paper is that individual Lyapunov function of each subsystem is constructed by flexibly adopting the upper and lower bounds of the control gain functions of each subsystem. Furthermore, by combining the average dwell-time scheme and the adaptive backstepping design, a valid adaptive neural state-feedback controller design algorithm is presented such that all the signals of the switched closed-loop system are in probability semiglobally uniformly ultimately bounded, and the tracking error eventually converges to a small neighborhood of the origin in probability. Finally, the availability of the developed control scheme is verified by two simulation examples. [ABSTRACT FROM AUTHOR]

This paper concentrates on the adaptive state-feedback quantized control problem for a class of multiple-input–multiple-output (MIMO) switched nonlinear systems with unknown asymmetric actuator dead-zone. In this study, we employ different quantizers for different subsystem inputs. The main challenge of this study is to deal with the coupling between the quantizers and the dead-zone nonlinearities. To solve this problem, a novel approximation model for the coupling between quantizer and dead-zone is proposed. Then, the corresponding robust adaptive law is designed to eliminate this nonlinear term asymptotically. A direct neural control scheme is employed to reduce the number of adaptive laws significantly. The backstepping-based adaptive control scheme is also presented to guarantee the system performance. Finally, two simulation examples are presented to show the effectiveness of our control scheme. [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]

In this paper, the consensus tracking problem is investigated for a class of continuous switched stochastic nonlinear multiagent systems with an event-triggered control strategy. For continuous stochastic multiagent systems via event-triggered protocols, it is rather difficult to avoid the Zeno behavior by the existing methods. Thus, we propose a new protocol design framework for the underlying systems. It is proven that follower agents can almost surely track the given leader signal with bounded errors and no agent exhibits the Zeno behavior by the given control scheme. Finally, two numerical examples are given to illustrate the effectiveness and advantages of the new design techniques. [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]

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 addresses the stability problem for a class of switched nonlinear systems subject to random disturbances whose $\tau $ -order moments ( \tau >1$ ) are finite. First, some general conditions are given to guarantee the existence and uniqueness of solutions to random switched systems. Next, these results are used to deduce the criteria of noise-to-state stability under probabilistic switching signal. Then, the average dwell-time approach is adopted to study the noise-to-state stability, the e^{\lambda t} -weighted (integral) noise-to-state stability and the global asymptotic stability of random switched systems. All the criteria on global existence and stability of solutions are developed by virtue of multiple Lyapunov functions. Finally, two numerical examples are given to demonstrate the validity of the theoretical results. [ABSTRACT FROM PUBLISHER]

Controlled distinguishability of two dynamical systems is the property of the systems that guarantees the existence of a control input generating different outputs of the systems regardless of their initial state vectors. These inputs are referred in the literature as discerning control inputs. In this paper, a necessary and sufficient condition for controlled distinguishability of continuous-time bilinear systems is established. It generalizes the classic one provided in the literature for the class of linear systems and a method for designing discerning inputs of bilinear systems that stabilize the systems is also proposed. [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]

This paper studies the stabilization problem via the co-design of controllers and a switching policy for a new class of nonstrict feedback switched nonlinear systems whose subsystems consist of a chain of integrators, feedback paths, and first-order feedforward paths. Designing only smooth feedback controllers cannot deal with the unstabilizable factors caused by feedforward paths. By exploiting the single control Lyapunov function method, an effective switching policy is co-designed to compensate the controllers. In addition, we present a generalized backstepping process, based on which the solvability of virtual controllers is guaranteed, the algebraic condition for stabilizability is identified, and the transient response of the closed-loop systems is improved. Two examples demonstrate the effectiveness. [ABSTRACT FROM AUTHOR]

This paper addresses the cooperative output regulation problem of linear multi-agent systems under switching communication topologies. A distributed event-triggered control scheme is proposed so that the cooperative output regulation problem is solved with only intermittent communication. The communication topology is not required to be connected at every time instant under the jointly connected assumption. With the proposed triggering mechanism, each agent only transmits the information to its neighbors at its own triggering times or the switching times. By introducing a fixed timer, Zeno behavior is strictly excluded for each agent. The effectiveness of the proposed control scheme is demonstrated by an example. [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]

The stability and stabilization problems for a class of switched discrete-time nonlinear systems are studied in this paper. Each nonlinear subsystem of the presented switched system is modeled as a piecewise affine (PWA) one by splitting the state space into polyhedron regions. With the aid of a simple searching strategy for active state transition pairs at a switching instant, i.e., the so-called $\mathbb {S}$ -arbitrary switching approach, the stability criteria are derived via the relaxed piecewise quadratic Lyapunov function technique. Then, using the descriptor system approach, a family of PWA stabilizing controllers are designed to guarantee exponential stability of the resulting closed-loop control system, and the corresponding PWA controller gains could be calculated using numerical software. The validity and potential of the developed techniques are verified through a numerical example. [ABSTRACT FROM AUTHOR]

Most of the existing characterizations of the integral input-to-state stability (iISS) property are not valid for time-varying or switched systems in cases where converse Lyapunov theorems for stability are not available. This paper provides a characterization that is valid for switched and time-varying systems, and shows that natural extensions of some of the existing characterizations result in only sufficient but not necessary conditions. The results provided also pinpoint suitable iISS gains and relate these to supply functions and bounds on the function defining the system dynamics. [ABSTRACT FROM PUBLISHER]

Multiple Lyapunov functions (MLFs)-based small-gain theorems are presented for switched interconnected nonlinear systems with unstable subsystems, which extend the small-gain technique from its original non-switched nonlinear version to a switched nonlinear version. Each low dimensional subsystem does not necessarily have the input-to-state stability (ISS) property in the whole state space, and it only has individual ISS property in some subregions of the state space. The novelty of this paper is that integral-type MLFs and small-gain techniques are utilized to establish some MLFs-based small-gain theorems for switched interconnected nonlinear systems, which derive various stability results under some novel switching laws designed and construct integral-type MLFs. The small-gain theorems proposed cover several recent results as special cases, which also permit removal of a common restriction in which all low dimensional subsystems in switched interconnected systems are ISS or only some are ISS and others are not. Finally, two illustrative examples are presented to demonstrate the effectiveness of the results provided. [ABSTRACT FROM AUTHOR]

We solve the problem of global uniform input-to-state stabilization of nonlinear switched systems with time-varying and periodic dynamics, with dynamic uncertainties, and with external disturbances. The switching signal is assumed to be unknown and the dynamics of the known components of the state vector is equivalent to the general triangular form (GTF) with non-invertible input-output maps. In our first and most general result, we prove that, if the dynamic uncertainty is treated as external disturbance, then the general triangular form system can be stabilized with arbitrarily small gain w.r.t. the dynamic uncertainty by means of a switching-independent, smooth and periodic feedback. Hence, using a suitable extension of the well-known small gain theorem to our case of switched systems with arbitrary switchings, we obtain the uniform input-to-state stabilization of the entire interconnected system. The second part of the paper addresses a more special case of triangular form (TF) switched systems with right-invertible input-output (I-O) maps with unknown switchings and with dynamic uncertainties. We show that the design becomes simpler and more constructive and the controllers become time-invariant if the dynamics is autonomous in this special case. Finally, we consider an example with explicit design of the stabilizing controllers. [ABSTRACT FROM PUBLISHER]

This paper investigates the problem of adaptive neural tracking control via output-feedback for a class of switched uncertain nonlinear systems without the measurements of the system states. The unknown control signals are approximated directly by neural networks. A novel adaptive neural control technique for the problem studied is set up by exploiting the average dwell time method and backstepping. A switched filter and different update laws are designed to reduce the conservativeness caused by adoption of a common observer and a common update law for all subsystems. The proposed controllers of subsystems guarantee that all closed-loop signals remain bounded under a class of switching signals with average dwell time, while the output tracking error converges to a small neighborhood of the origin. As an application of the proposed design method, adaptive output feedback neural tracking controllers for a mass-spring-damper system are constructed. [ABSTRACT FROM PUBLISHER]