Lmi-Based Robust H_∞ Control And Application For Uncertain System

In a practical control system, there always exist possibly multiple sources of uncertainties. The differences between models and reality are often inevitable and be called modeling errors. It is difficult to obtain expected performance based on this kind of models. The analysis and synthesis problem for uncertain system is dealt with by introducing a new method.At first, robust H∞performance analysis is researched in this paper. Based on Lyapunov function method and the Schur complement lemma, extended H∞performance criterion is provided by‘small scalar method’. Different from the classical bounded real lemma, this criterion realizes the elimination of the product between the system matrices and Lyapunov matrices by introducing some loose variable. Based on it, a sufficient condition for the existence of a state-feedback controller is formulated in terms of LMIs. The corresponding controller design is cast into a convex optimization problem. Then we consider the state observer design and observer-based H∞control problem. The purpose is to guarantee the augmented system asymptotically stable and satisfy the H∞performance index. A simulation example about a vibration isolation platform system is provided to show the effectiveness of the proposed control design method...