A Study On Robust And Guaranteed Cost Control For Uncertain Systems

Uncertainty and time-delay exist in real industrial process systems, The introduction of uncertainty of the system describes the difference between the mathematic model and controlled plant, which reflects the existing of the variation of the system parameters and disturbance. In a word, it is of a great importance in theoretical and practical. The robust control theory is an effective way to deal with the uncertainty parameters, However, it' s not enough to just satisfy the robust stability. Linear quadratic performance (guaranteed cost performance) criterion can reflect a lot of performance requirements, therefore, how to design a guaranteed cost controller under which the closed-loop system is asymptotically stable for all admissible uncertainty and the closed-loop cost function value is not more than a specified upper bound has drawn considerable attention.Based on Lyapunov theory H₂/H_∞ control theory and convex set theory, linear matrix inequality method is adopted in this paper to study the robust and guaranteed cost control problem for uncertain systems. The main contents are as follows:1. For A class of linear system with H₂ and H_∞ quality constraints, a memoryless state feedback control law is derived. The results are given in the terms of linear matrix inequality, A simulation example demonstrates that mixed H₂/H_∞ control is effective to the disturbance attenuation.2. Linear discrete systems with norm-bounded uncertainties are discussed, design its robust controller with H₂ and H_∞ quality constraints. Based on linear matrix inequality method, a solving scheme...