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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]

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]