基于观测器的不确定T-S模糊系统鲁棒镇定

Observer-based robust stabilization of uncertain T-S fuzzy systems

为带有参数不确定性的T-S模糊控制系统提出了新的基于观测器的鲁棒输出镇定条件.该条件用来设计模糊控制器和模糊观测器.为了设计模糊控制器和模糊观测器,用T-S模糊模型来表示非线性系统,并运用平行分布补偿观念.充分条件基于二次Lyapunov函数,通过将模糊系统的鲁棒镇定条件表述为一系列矩阵不等式,比以往文献中列出的条件具有更小的保守性.该不等式为双线性矩阵不等式,可分两步骤先后解得使T-S模糊系统镇定的控制器增益和观测器增益.最后,通过对一个具有不确定性的连续时间非线性系统控制的例子证明了提出方法比以往方法更宽松.

This paper proposes new observer-based output robust stabilization conditions for Takagi-Sugeno（T-S） fuzzy control systems with parametric uncertainties.They are applied to design problems of fuzzy controllers and fuzzy observers.To design fuzzy controller and fuzzy observers,nonlinear systems are represented by T-S fuzzy models and the concept of parallel distributed compensation is employed.The sufficient condition is based on the quadratic Lyapunov function and is less conservative than some conditions published recently in the literature by describing the robust stabilization condition through a set of matrix inequalities.The sufficient condition is formulated in the format of bilinear matrix inequalities;one can obtain successively the controller gains and observer gains of T-S fuzzy control system with parametric uncertainties using two-step procedure.Finally,it is successfully demonstrated that the proposed approach is a more relaxed condition than others in the control of a continuous-time nonlinear uncertain system.