STUDY ON GENERAL STABILITY AND STABILIZABILITY OF LINEAR DISCRETE-TIME STOCHASTIC SYSTEMS

With the aid of spectrum technique, a new concept called D(0,alpha)stabilizability (0 < alpha <= 1) is introduced, for which a necessary and sufficient condition is also proposed via a linear matrix inequality (LMI)-based approach. Especially, D( 0, alpha)-stabilizability is identical with asymptotic mean square stabilizability when alpha = 1. A more general regional stability called D-R-stability is discussed extensively and some concrete examples are given. As applications, the relationship among D( 0, alpha; beta)-stability, the decay rate of the system state response and the second-order moment Lyapunov exponent L-e(2) is revealed.