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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 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]

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]

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 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]

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]

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]