Xiongping Dai

Almost Sure Stability of Discrete-Time Switched Linear Systems: A Topological Point of View

In this paper, we study the stability of discrete-time switched linear systems via symbolic topology formulation and the multiplicative ergodic theorem. A sufficient and necessary condition for

Criteria of Stability for Continuous-Time Switched Systems by Using Liao-Type Exponents

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Pointwise Stability of Discrete-Time Stationary Matrix-Valued Markovian Processes

-almost sure stability is derived, where

Almost sure stability of discrete-time switched linear systems

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Chaotic behavior of discrete-time linear inclusion dynamical systems

is the Parry measure of the topological Markov chain with a prescribed transition (0,1)-matrix

Topological formulation of discrete-time switched linear systems and almost sure stability

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Brief paper: Periodically switched stability induces exponential stability of discrete-time linear switched systems in the sense of Markovian probabilities

. The obtained

A Gel’fand-type spectral radius formula and stability of linear constrained switching systems☆

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Realization of joint spectral radius via Ergodic theory

-almost sure stability is invariant under small perturbations of the system. The topological description of stable processes of switched linear systems in terms of Hausdorff dimension is given, and it is shown that our approach captures the maximal set of stable processes for linear switched systems. The obtained results cover the stochastic Markov jump linear systems, where the measure is the natural Markov measure defined by the transition probability matrix. Two examples are provided to illustrate the theoretical outcomes of the paper.

The finite-step realizability of the joint spectral radius of a pair of d×d matrices one of which being rank-one☆

For a given continuous-time switched system, its stability is determined by (i) the structure of the system; (ii) the admissible switching set; and (iii) the duration time in each subsystem. Both (ii) and (iii) are stability characterizations of switching dynamics for continuous-time switched systems. In this paper, we introduce a new type of characteristic exponent, the Liao-type exponent, which is computable, to capture the stability feature of continuous-time switched systems. We obtain two criteria of asymptotic exponential stability for linear and nonlinear cases by estimating the corresponding Liao-type exponents, respectively. The proposed approach is constructive and the obtained results allow existence of switching constraints. Several examples are provided to illustrate theoretical outcomes of the paper.