不确定模糊系统具有指定衰减率的鲁棒保成本控制

Robust guaranteed cost control with appointed decay rate for uncertain fuzzy systems

结合系统响应速度的考虑,讨论由T-S模糊模型描述的不确定连续非线性系统具有指定衰减率的鲁棒保成本控制问题.基于扩展稳定性条件和等价投影引理,导出系统鲁棒保成本控制器存在的充分条件,并可将此控制器的最优设计问题转化为一组线性矩阵不等式的凸优化问题.研究表明:所设计的控制器不仅能保证闭环不确定模糊系统以衰减率α鲁棒渐近稳定,而且还给出了保成本上界的一个优化值.最后,数值示例验证了该设计方法的有效性.

Combining with the performance of system response rate, the problem of robust guaranteed cost control with appointed decay rate is discussed for uncertain continuous-time nonlinear systems described by Takagi-Sugeno （T-S） fuzzy model. Based on the relaxed stability condition and reciprocal projection lemma, a sufficient condition for the existence of robust guaranteed cost controller is derived. And the design of optimal guaranteed cost controller can be reduced to a convex optimization problem in terms of linear matrix inequalities （LMIs）. It is shown that the designed controller not only guarantees the robust asymptotic stability with decay rate a of the closed-loop uncertain fuzzy system, but also provides an optimized guaranteed cost upper bound. At last, a numerical example is given to illustrate the effectiveness of the design procedure.