Based On The Uncertainty Of Bmi Method Robust Guaranteed Cost Control Of Discrete Time-delay Systems

In recent years, with the rapid development of pulse techniques, digital computer, digital control system has replaced analog control systems in military, aerospace, and industrial process control. Discrete systems is becoming increasingly important as a basis for the design and analysis of digital control systems. In order to achieve satisfactory control performance for the actual systems, the design controllers can stabilize the uncertain discrete-time delay system and meanwhile guarantee a specified level of the quadratic cost function. Since time delays and uncertainties in physical models are important factors of instability and poor performance, the robust guaranteed cost control problem for uncertain discrete-time delay system has received considerable attention during the past decades.The robust guaranteed cost control via memoryless state feedback and static output feedback for uncertain discrete-time delay system is considered in this paper. Sufficient conditions for the existence of the robust guaranteed cost controllers are expressed as bilinear matrix inequality(BMI). Furthermore, the design methods of optimal robust guaranteed cost controllers which minimize the upper bound of a given quadratic cost function are presented. Alternate iterative algorithms are proposed to solve the nonconvex optimization problems with BMI constrains. The nonconvex problems with BMI constrains are converted to the feasible and generalized eigenvalue problems with LMI constrains which can be solved conveniently by using Matlab LMI Control Toolbox.Based on Lyapunov stability theory, the problem of robust guaranteed cost decentralized stabilization for uncertain discrete large-scale systems with delays is also investigated in this paper. The robust guaranteed cost decentralized controllers via memoryless state feedback and static output feedback are expressed as bilinear matrix inequalities(BMIs). Furthermore, alternate iterative algorithms are proposed to design the controllers. Numerical examples are given to illustrate effectiveness of proposed methods.