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

摘要

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 H-infinity state feedback controllers such that the system with admissible uncertainties is not only quadratically internally stable but also robust H-infinity controllable. A sufficient condition for the existence of the desired robus H-infinity controller is obtained. Finally, an example with simulations is given to verify the effectiveness of our theoretical results.