D Stability Of Discrete Time Delay Systems And H_ ¡Þ Constrained Output Feedback Control

Based on Lyapunov stability theory, D-stable theory and H∞control theory, with bilinear matrix inequality (BMI), linear matrix inequality (LMI) and matrix analysis as the mathematical tools, this paper studies discrete time-delay systems with constraints on pole placement and H∞attenuation level. A BMI formulation is first given for output feed-back control problem, and then an effective algorithm is proposed to solve the desired output feedback gain. The main researches include:(1) D-stabilization problem of a class of discrete systems with time-delay is studied. A sufficient condition for the solvability of the problem is formulated in the feasibility of a set of BMIs. And an LMI-based iterative algorithm is given to solve the associated BMIs numerically.(2) For discrete systems with time-delay, H-infinity output-feedback is studied, a BMI sufficient condition is provided, and an LMI-based iterative algorithm is also provided to solve the BMI problem.(3) For discrete systems with time-delay, H-infinity output-feedback problem with D-stable constraints is studied. For the solvability of the problem, a sufficient BMI condition is given. An LMI-based iterative algorithm is provided to find a satisfactory output-feedback gain.For the three problems above, based-on theories and algorithms provided, some numerical examples are provided.