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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]

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 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]

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 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]

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]

We study feedback control for a discrete-time integrator with unitary delay in the presence of quantization both in the control action and in the measurement of the controlled variable. In some applications the quantization effects can be neglected, but when high precision is needed, they have to be explicitly accounted for in control design. In this paper, we propose a switched control solution for minimizing the effect of quantization of both the control and controlled variables for the considered system, that is quite common in the computing systems domain, for example, in thread scheduling, clock synchronization, and resource allocation. We show that the switched solution outperforms the one without switching, designed by neglecting quantization, and analyze necessary and sufficient conditions for the controlled system to exhibit periodic solutions in the presence of an additive constant disturbance affecting the control input. Simulation results provide evidence of the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stability problem of randomly switched systems. By using the probability analysis method, the almost surely globally asymptotical stability and almost surely exponential stability are investigated for switched systems with semi-Markovian switching, Markovian switching, and renewal process switching signals, respectively. Two examples are presented to demonstrate the effectiveness of the proposed results, in which an example of consensus of multiagent systems with nonlinear dynamics is taken into account. [ABSTRACT FROM AUTHOR]

This paper focuses on the stability analysis and control of adaptive switching systems by establishing Lyapunov-based logic switching rules. Through considering performance-index-based adaptive switching control under a general framework, sufficient conditions are proposed and proved to ensure global generalized exponential stability and global finite-time stability. By taking these conditions as guidelines for designing control laws and logic switching rules, we explore their applications in controlling a class of lower-triangular nonlinear systems with an unknown control direction. [ABSTRACT FROM AUTHOR]

This paper is concerned with dynamic output feedback control for a class of switched systems with mode-dependent average dwell-time switching. By constructing a quasi-time-dependent Lyapunov function, the issues of global uniform asymptotic stability and $\ell _{2}$ -gain analysis for the switched system are addressed first. Then, a set of reduced-order output feedback controllers is designed, which is both mode-dependent and quasi-time-dependent. Compared with time-independent criteria, the new results greatly reduce the conservatism. The effectiveness and merits of the proposed method are illustrated with a numerical example. [ABSTRACT FROM AUTHOR]

This paper deals with the exponential stabilization problem of discrete-time Markovian jump systems via a hybrid control strategy, in which the transition probability matrix and static output-feedback controller are designed simultaneously. A necessary and sufficient condition for the existence of an exponential stabilizing transition probability matrix is derived by means of a mode-dependent parametric approach. Furthermore, a sufficient condition is established for the above-mentioned hybrid design with a specified lower bound on the decay rate. The proposed design approaches can be applied to solve two kinds of control design problems with practical constraints imposed on the hybrid design. Besides, an estimation approach is proposed on the decay rate and decay coefficient of the jump systems. Also, two optimization problems are formulated to obtain the hybrid control strategy. Finally, two numerical examples and a network-on-chip based application are provided to illustrate the effectiveness of the proposed results. [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]

This paper introduces the notion of common zeroing-output systems (CZOS) to analyze the stability of switched systems. The concept of CZOS allows one to verify weak zero-state detectability. It characterizes a common behavior of any individual subsystem when the output signal for each subsystem is “approaching” zero. Heuristically speaking, it removes the effect of switching behavior, and thus enables one to analyze stability properties in systems with complex switching signals. With the help of CZOS, the Krasovskii–LaSalle theorem can be extended to switched nonlinear time-varying systems with both arbitrary switching and more general restricted switching cases. For switched nonlinear time-invariant systems, the needed detectability condition is further simplified, leading to several new stability results. Particularly, when a switched linear time-invariant system is considered, it is possible to generate a recursive method, which combines a Krasovskii–LaSalle result and a nested Matrosov result, to find a CZOS if it exists. The power of the proposed CZOS is demonstrated by consensus problems in literature to obtain a stronger convergence result with weaker conditions. [ABSTRACT FROM AUTHOR]

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]

In this paper, the problem of stability on stochastic systems with state-dependent switching is investigated. To analyze properties of the switched system by means of Itô's formula and Dynkin's formula, it is critical to show switching instants being stopping times. When the given active-region set can be replaced by its interior, the local solution of the switched system is constructed by defining a series of stopping times as switching instants, and the criteria on global existence and stability of solution are presented by Lyapunov approach. For the case where the active-region set can not be replaced by its interior, the switched systems do not necessarily have solutions, thereby quasi-solution to the underlying problem is constructed and the boundedness criterion is proposed. The significance of this paper is that all the results presented depend on some easily-verified assumptions that are as elegant as those in the deterministic case, and the proofs themselves provide design procedures for switching controls. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of designing time-varying quantizers for the stabilization of switched linear systems with quantized output and switching delays. The detection delays of switches are assumed to be time-varying but bounded, and the dwell time of the switching signal is assumed to be larger than the maximum delay. Given a switching controller, we analyze reachable sets of the closed-loop state by using a common Lyapunov function and then construct a quantizer that guarantees asymptotic stability. A sufficient condition for the existence of such a quantizer is characterized by the maximum switching delay and the dwell time. [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]

In this paper, we introduce continuous-time linear compartmental switched systems and investigate their stability and stabilizability properties. By their nature, these systems are always stable. Necessary and sufficient conditions for asymptotic stability for arbitrary switching functions, and sufficient conditions for asymptotic stability under certain dwell-time conditions on the switching functions are proposed. Finally, stabilizability is thoroughly investigated and proved to be equivalent to the existence of a Hurwitz convex combination of the subsystem matrices, a condition that, for positive switched systems, is only sufficient for stabilizability. [ABSTRACT FROM AUTHOR]

Recently a special hybrid system called Switching Markov Jump Linear System (SMJLS) is studied. A SMJLS is subject to a deterministic switching and a stochastic Markovain switching. To extend the results already obtained and to investigate some new aspects of such systems, our main contributions in this paper are: i) Transient analysis of Markov process, i.e., the expectations of the sojourn time, the activation number of any mode, and the number of switchings between any two modes and ii) two sufficient conditions of the exponential almost sure stability for a general SMJLS. Different from previous work, which is a special case of our study, the transition rate matrix for the random Markov process in our study is not fixed, but varies when a deterministic switching takes place. [ABSTRACT FROM AUTHOR]

This paper is concerned with the derivation of a model reference adaptive control (MRAC) scheme for multimodal piecewise-affine (PWA) and piecewise-linear systems. The control allows the plant to track asymptotically the states of a multimodal piecewise affine (or smooth) reference model. The reference model can be characterized by a number and geometry of phase space regions that can be entirely different from those of the plant. Numerical simulations on a set of representative examples confirm the theoretical derivation and proof of stability. [ABSTRACT FROM AUTHOR]

In this paper, we first establish a stability result for a class of linear switched systems involving Kronecker product. The problem is interesting in that the system matrix does not have to be Hurwitz at any time instant. This class of linear switched systems arises in the control of multi-agent systems under switching network topology. As applications of this stability result, we give the solvability conditions for both the leaderless consensus problem and the leader-following consensus problem for general marginally stable linear multi-agent systems under switching network topology. In contrast with some existing results, our results only assume that the dynamic graph is uniformly connected. [ABSTRACT FROM AUTHOR]

In this paper we consider the class of discrete-time switched systems switching between p autonomous positive subsystems. First, sufficient conditions for testing stability, based on the existence of special classes of common Lyapunov functions, are investigated, and these conditions are mutually related, thus proving that if a linear copositive common Lyapunov function can be found, then a quadratic positive definite common function can be found, too, and this latter, in turn, ensures the existence of a quadratic copositive common function. Secondly, stabilizability is introduced and characterized. It is shown that if these systems are stabilizable, they can be stabilized by means of a periodic switching sequence, which asymptotically drives to zero every positive initial state. Conditions for the existence of state-dependent stabilizing switching laws, based on the values of a copositive (linear/quadratic) Lyapunov function, are investigated and mutually related, too. [ABSTRACT FROM PUBLISHER]

This paper considers asymptotic stability and transient performance of discrete-time piecewise affine systems. We propose a procedure to construct a nested sequence of finite-state symbolic models, each of which abstracts the original piecewise affine system and leads to linear matrix inequalities for guaranteed stability and performance levels. This sequence is in the order of decreasing conservatism, and hence gives us the option to pay more computational cost and analyze a finer symbolic model within the sequence in return for less conservative results. Moreover, in the special case where this sequence is finite, an exact analysis of stability and performance is achieved via semidefinite programming. [ABSTRACT FROM PUBLISHER]

We consider the problem of achieving input-to-state stability (ISS) with respect to external disturbances for control systems with quantized measurements. Quantizers considered in this paper take finitely many values and have an adjustable “center” and “zoom” parameters. Both the full state feedback and the output feedback cases are considered. Similarly to previous techniques from the literature, our proposed controller switches repeatedly between “zooming out” and “zooming in.” However, here we use two modes to implement the “zooming in” phases, which allows us to attenuate an unknown disturbance while using the minimal number of quantization regions. Our analysis is trajectory-based and utilizes a cascade structure of the closed-loop hybrid system. We further show that our method is robust to modeling errors using a specially adapted small-gain theorem. The main results are developed for linear systems, but we also discuss their extension to nonlinear systems under appropriate assumptions. [ABSTRACT FROM PUBLISHER]

The twisting and supertwisting algorithms, generating important classes of second order sliding modes (SOSMs), are well-recognized for their finite time stability and robustness properties. In the present paper, a continuous modification of the twisting algorithm and an inhomogeneous perturbation of the supertwisting algorithm are introduced to extend the class of SOSM's that present the afore-mentioned attractive features. Thus modified, the twisting and supertwisting algorithms are utilized in the state feedback synthesis and, respectively, velocity observer design, made for the finite time stabilization of a double integrator if only output measurements are available. Performance and robustness issues of the resulting output feedback synthesis are illustrated by means of numerical simulations. [ABSTRACT FROM AUTHOR]