Convergence rate analysis of discrete-time Markovian jump systems

This paper is concerned with convergence rate analysis of a discrete-time Markovian jump linear system. First, two eigenvalue sets of some operator associated with the Markovian jump linear system are defined to characterize its stability. It is shown that the fastest and slowest convergence rate of the Markovian jump system can be determined by the eigenvalues having minimal modulus and maximal modulus, respectively. Finally, a linear matrix inequality based approach is established to design controllers such that the closed-loop system has a guaranteed convergence rate. A numerical example is carried out to illustrate the effectiveness of the proposed approach.