The problem of guaranteed cost control is investigated for a class of discrete-time saturated switched systems. The purpose is to design the switched law and state feedback control law such that the closed-loop system is asymptotically stable and the upper-bound of the cost function is minimized. Based on the multiple Lyapunov functions approach, some sufficient conditions for the existence of guaranteed cost controllers are obtained. Furthermore, a convex optimization problem with linear matrix inequalities (LMI) constraints is formulated to determine the minimum upper-bound of the cost function. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.

中文翻译：

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离散时间切换饱和系统的有保证的成本控制

针对一类离散时间饱和切换系统，研究了保证成本控制的问题。目的是设计开关定律和状态反馈控制定律，以使闭环系统渐近稳定，并使成本函数的上限最小化。基于多重李雅普诺夫函数方法，为保证成本控制器的存在提供了一些充分条件。此外，提出了具有线性矩阵不等式（LMI）约束的凸优化问题，以确定成本函数的最小上限。最后，通过数值例子说明了该方法的有效性。