Robustly exponentially almost sure stabilization of uncertain discrete‐time composite switched systems

Abstract This paper is concerned with the robustly exponentially almost sure (EAS) stabilization of uncertain discrete‐time composite switched systems (CSSs), in which the dominant signal subjects to a semi‐Markov chain, while the subordinate signals follow a family of different Markov chains. Norm‐bounded uncertainties impacting the state and input matrices of the system are taken into account. Utilizing numerical computation methods, bounds on the transient statistical properties of Markov chain are provided. Based on this, sufficient conditions for robustly EAS stabilization are established by combining an estimate of the sojourn time for modes in a semi‐Markov chain. Our result is the discrete counterpart of prior work concerning continuous‐time dual‐switching systems. Two examples are provided to validate the effectiveness of developed results.