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基于线性矩阵不等式和保成本控制理论,研究了一类具有执行器饱和的不确定离散切换线性系统在任意切换下的保成本控制及优化设计问题。系统矩阵和输入矩阵中含有时变不确定性。目的是设计状态反馈控制律使得闭环系统渐近稳定的同时,使得所给定的成本函数的上界最小。首先,利用共同李雅普诺夫函数方法,获得了状态反馈保成本控制器存在的充分条件。进一步,为获得使得成本函数上界最小的优化设计方案,将确定成本函数最小上界的问题转化为带有线性矩阵不等式约束的凸优化问题。这种检验方法容易计算,适合在工程中使用。最后,最后通过一个数值例子验证了所提出方法的有效性。
Based on the theory of linear matrix inequality and guaranteed cost control, the guaranteed cost control and optimal design of a class of uncertain discrete switched linear systems with actuator saturation under arbitrary switching are studied. System matrices and input matrices contain time-varying uncertainties. The purpose is to design the state feedback control law such that the closed-loop system is asymptotically stable and minimizes the upper bound of the given cost function. First, the sufficient condition for existence of guaranteed cost controller with state feedback is obtained by using the common Lyapunov function method. Further, in order to obtain the optimal design scheme that minimizes the upper bound of the cost function, the problem of determining the minimum upper bound of the cost function is transformed into a convex optimization problem with linear matrix inequality constraints. This test method is easy to calculate, suitable for use in engineering. Finally, a numerical example is given to verify the effectiveness of the proposed method.