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

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