Robust H∞ control for switched singular linear systems with uncertainties in the derivative matrices: an improved average dwell time approach

This paper addresses the robust H_∞ control problem for continuous‐time switched singular systems with uncertainties in the state, input, and derivative matrices. A two‐phase method is proposed in this paper to optimize H_∞ performance and to minimize the upper bound of the average dwell time. First, sufficient conditions for finding a state feedback controller guaranteeing the minimum H_∞ disturbance attenuation are proposed. Besides, the average dwell time is obtained by solving linear matrices inequalities introduced in this paper. Second, to minimize the upper bound of the average dwell time, an improve average dwell time approach is put forward by introducing a new technique. And based on the result in the first phase, a new feedback controller, which optimizes H_∞ performance and minimizes the upper bound of the average dwell time is obtained by using the improved average dwell time approach. The point is that when the upper bound of the average dwell time is decreasing, H_∞ disturbance attenuation will increase and vice versa. Therefore, a trade‐off should be built between H_∞ disturbance attenuation and average dwell time in practice. Finally, several numerical examples are presented to illustrate the effectiveness of the methods proposed. Copyright © 2015 John Wiley & Sons, Ltd.