H∞ control of a class of 2-D continuous switched delayed systems via state-dependent switching

This paper addresses the problem of state feedback H∞ stabilisation of 2-D (two-dimensional) continuous switched state delayed systems represented by the Roesser model using the multiple Lyapunov functional approach. First, an asymptotical stability condition of 2-D continuous switched systems with state-dependent switching is derived. Second, a sufficient condition for H∞ performance of the underlying system is established. Third, a state feedback controller is proposed to ensure that the resulting closed-loop system has a prescribed H∞ performance level under a state-dependent switching signal. All the results are developed in terms of linear matrix inequalities. Finally, three examples are provided to demonstrate the validity and effectiveness of the proposed method.