多时滞不确定广义系统的非脆弱H_∞保成本控制

Non-fragile H_∞ Guaranteed Cost Control for Uncertain Singular Systems with Multiple Time-Delay

对一类具有结构不确定性的线性多时滞广义系统,结合了一个二次性能指标,研究其非脆弱H∞保成本控制律的设计问题.基于Lyapunov稳定性理论证明其系统的稳定性.利用线性矩阵不等式(LMI)方法,分别对控制器增益具有加法式摄动和乘法式摄动两种情形加以讨论,得到非脆弱保成本控制律设计的一个充分条件.该控制器能保证闭环系统稳定和一定的线性二次性能指标上界,同时具有H∞范数下的干扰抑制作用.最后,针对加法和乘法两种摄动的情况,用数值例子进一步说明本文所给方法的有效性.

Discusses the design problem of non-fragile guaranteed cost controller for a class of linear multiple time-delay singular systems with structural uncertainties. A linear quadratic cost function is considered as a performance measure. A sufficient condition is given in terms of LMIs （linear matrix inequalities） for the existence of the non-fragile H∞ guaranteed cost controllers in cases of both additive and multiplieative perturbation. The controller guarantees the robust stability of the closed-loop system, and the upper bound of quadratic performance index satisfies the Hoo disturbance attenuation level. A numerical example for both eases is given to illustrate the effectiveness of the theory.