Regional stability and stabilizability of linear stochastic systems: Discrete-time case

By means of the spectral analysis technique of the generalized Lyapunov operator, a new kind of regional stabilizability named "D(0, α)-stabilizability" (0 <; α _≤ 1) is introduced, for which, a necessary and sufficient condition is proposed via linear matrix inequality (LMI)-based approach. Moreover, a more general regional stability called "D_R-stability" is also discussed extensively and some interesting concrete examples are given. Finally, the relationship among D(0, α; β)-stability, the decay rate of the system state response and the second-order moment Lyapunov exponent L_e² is revealed, wsystem state responsehich can be regarded as the discrete-time version of the result corresponding to continuous-time stochastic systems.