In this paper we connect various topological and probabilistic forms of stability for discrete-time Markov chains. These include tightness on the one hand and Harris recurrence and ergodicity on the other. We show that these concepts of stability are largely equivalent for a major class of chains (chains with continuous components), or if the state space has a sufficiently rich class of appropr...

In 1892, the general problem of stability by the first approximation was considered by Lyapunov. He proved that if the system of the first approximation is regular and all its Lyapunov exponents (or characteristic exponents) are negative, then the solution of the original system is asymptotically Lyapunov stable. In 1930, it was stated by O. Perron that the requirement of regularity of the firs...

This paper derives some sufficient conditions for asymptotic stability of neural networks with constant or time-varying delays. The Lyapunov–Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) approach are employed to investigate the problem. It shows how some well-known results can be refined and generalized in a straightforward manner. For ...

This thesis deals with the stability analysis of switched linear systems. Such systems are characterised by a mixture of continuous dynamics and logic-based switching between discrete modes. This system class appears in a large variety of control systems and has a wide field of applications in the modern industrial society. While the application of switched control systems can be very beneficia...

Abstract. In this paper, we discuss stability properties of positive descriptor systems in the continuous-time as well as in the discrete-time case. We present characterisations of positivity and establish generalised stability criteria for the case of positive descriptor systems. We show that if the spectral projector onto the finite deflating subspace of the matrix pair (E, A) is nonnegative,...

This paper deals with the problem of delay-dependent stability criterion of uncertain periodic switched recurrent neural networks with time-varying delays.When uncertain discrete-time recurrent neural network is a periodic system, it is expressed as switched neural network for the finite switching state. Based on the switched quadratic Lyapunov functional approach SQLF and freeweighting matrix ...

In this paper, the problem of stability criteria for Markovian jumping BAM neural networks with leakage and discrete delays has been investigated. Some new sufficient condition are derived based on a novel Lyapunov-Krasovskii functional approach. These new criteria based on delay partitioning idea are proved to be less conservative because free-weighting matrices method and a convex optimizatio...

Complete results for the delay-dependent robust stability and feedback stabilization of linear neutral systems with unknown-but-bounded uncertainties are developed. New linear matrix inequalities-based delay-dependent stability criteria are derived in a systematic way using a new expanded state-space representation and a new Lyapunov-Krasovskii functional. The results are established without re...

This paper studies the problem of delay-range-dependent stability for continuous-time system with interval delay. Based on the dividing of the delay and reciprocally convex combination technique, some new delaydependent stability conditions are derived by constructing a novel Lyapunov functional. These criteria are expressed as a set of linear matrix inequalities (LMIs), which can be checked us...