Spectral characterisation for stability and stabilisation of linear stochastic systems with markovian switching and its applications

This study is concerned with the stability analysis and stabilisation of linear stochastic systems with Markovian switching by using the spectral technique. The notion of spectrum for Markovian jump linear stochastic systems (MJLSSs) is introduced and the relationship between the spectrum and the asymptotical mean-square stability is revealed. As applications, a necessary and sufficient condition for regional stability of MJLSSs and a result on generalised Lyapunov equations are derived. Examples are presented to illustrate the results established.