Linear discrete-time systems with Markovian jumps and mode dependent time-delay: Stability and stabilizability

Abstract

This paper considers stochastic stability and stochastic stabilizability of linear discrete-time systems with Markovian jumps and mode-dependent time-delays. Linear matrix inequality (LMI) techniques are used to obtain sufficient conditions for the stochastic stability and stochastic stabilizability of this class of Systems. A control design algorithm is also provided. A numerical example is given to demonstrate the effectiveness of the obtained theoretical results.