Almost sure stability for a class of dual switching linear discrete‐time systems

Abstract

Summary In this paper, a dual switching discrete‐time linear system, simultaneously subject to deterministic switching and Markov chain, is considered. This study does not consider the transition probability of the Markov chain as fixed but determined by the current position of deterministic switching. Namely, such dual switching discrete‐time linear system is composed of a family of discrete‐time Markov jump systems and follows a rule that directs the switching sequences between them. The exponentially almost sure stability problem, for dual switching discrete‐time linear system with exponential uncertainty, is addressed by using persistent dwell time and stochastic multi‐Lyapunov function. The sufficient conditions for the exponentially almost sure stability of dual switching discrete‐time linear system are expressed as linear matrix inequalities. Finally, a simulation example demonstrates the validity of the derived results.

Adaptive neural network prescribed performance control for dual switching nonlinear time-delay system

“…The almost sure stability for discrete dual switching system and continuous dual switching system is studied respectively in Refs. 8 – 10 .…”

“…As the switching mechanisms for practical applications are becoming more and more complex and the requirements for the system are higher, the transient performance of the system has attracted widespread attention. To achieve the prescribed performance, the studies for switched systems mainly used neural network adaptive control 11 , 12 , dynamic surface control 8 , 13 , fuzzy control 14 – 17 and other schemes 18 . Time-delay, as an important factor affecting system performance, is also widespread in practical systems.…”

Adaptive neural network control for uncertain dual switching nonlinear systems

“…Dual switching system (DSS) was introduced as a framework for modeling hybrid systems 4 . It’s a new type of system with both deterministic and stochastic signals 5 , 6 . The research of dual switching systems has mainly focused on the stability of the systems.…”