Stochastic Stabilization for Discrete-Time System with Input Delay and Multiplicative Noise in Control Variable

Abstract

The stabilization problems for time-delay stochastic systems with multiplicative noise in the control variable are investigated in this paper. The innovative contributions are described as follows. Since the past work on stabilization is based on some delay-dependent algebraic Riccati equation (DARE), how to numerically calculate the stabilizing solution remains an unsolved and open problem. On the one hand, an iterative algorithm for computing the unique stabilizing solution of DARE is proposed, while the convergence property is also proved. On the other hand, the concepts of critical stabilization and essential destabilization are proposed as a supplement to stochastic stabilization in terms of spectrum technique. Moreover, the Lyapunov-based necessary and sufficient conditions are developed.