Robust Quadratic Stabilizability and Control of Uncertain Linear Discrete-Time Stochastic Systems with State Delay

This paper mainly discusses the robust quadratic stability and stabilization of linear discrete-time stochastic systems with state delay and uncertain parameters. By means of the linear matrix inequality (LMI) method, a sufficient condition is, respectively, obtained for the stability and stabilizability of the considered system. Moreover, we design the robust state feedback controllers such that the system with admissible uncertainties is not only quadratically internally stable but also robust controllable. A sufficient condition for the existence of the desired robust controller is obtained. Finally, an example with simulations is given to verify the effectiveness of our theoretical results.