Exponential L1L1 output tracking control for positive switched linear systems with time-varying delays

The problem of exponential L1L1 output tracking control for positive switched linear systems with time-varying delays is addressed in this paper. The exponential L1L1-gain performance index is introduced to study such a problem. By resorting to the average dwell time approach, and also by constructing an appropriate piecewise co-positive type Lyapunov–Krasovskii functional, a new delay-dependent exponential stability criterion is developed, and the exponential L1L1-gain performance is analyzed. Based on the results obtained, a state feedback controller is constructed such that the exponential L1L1 output tracking performance is satisfied. A numerical example is given to demonstrate the effectiveness of the proposed method.