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针对一类具有时变时滞的奇异脉冲切换系统,研究鲁棒弹性保成本控制问题.首先,基于多Lyapunov泛函技术,建立标称自由系统具有正则性、因果性及渐近稳定性的充分条件.然后,给出一个弹性保性能控制器的设计方案,该方案能保证对所有容许的不确定性,闭环系统是正则的、因果的和渐近稳定的,且成本函数不超过某个上界.并进一步运用矩阵最大奇异值的最小化方法和凸优化方法,求解最优鲁棒弹性保成本控制器.所有的充分条件均巧妙地表示为线性矩阵不等式形式.最后,运用两个仿真实例验证本研究方法较少的保守性和有效性.
Aiming at a class of singular pulse switching systems with time-varying delays, the robust elastic guaranteed cost control problem is studied.Firstly, based on the multi-Lyapunov functional theory, the establishment of a nominal free system with sufficient regularity, causality and asymptotic stability Then, a design scheme of elastic guaranteed cost controller is given, which ensures that the closed-loop system is regularized, causal and asymptotically stable to all permissible uncertainties and the cost function does not exceed a certain upper limit And further use the minimization method and convex optimization method of the maximum matrix singular value to solve the optimal robust elastic guaranteed cost controller.All the sufficient conditions are subtly expressed as the form of linear matrix inequalities.Finally, Verify that this method is less conservative and effective.