Stochastic stability and stabilization of Markov jump linear systems with fixed dwell time and unknown transition rates

This paper investigates the stochastic stability and stabilization of Markov jump linear systems(MJLSs) with fixed dwell time (FDT) and partially known or completely unknown transition rates. By constructing an auxiliary system that originated from the initial system with state jumps, some stochastic stability criteria in terms of LMIs for MJLSs with FDT are established with both partially known or completely unknown transition rates. Based on multiple piecewise quadratic Lyapunov functions (MPQLFs) and vertex method, state feedback controllers are designed to stabilize the MJLSs with FDT and unknown transition rates by solving LMIs. Finally, a numerical example is given to illustrate the viability of our results.