Dynamic Output Feedback Control of Switched Repeated Scalar Nonlinear Systems

Abstract

The goal of this paper is to provide a solution to dynamic output feedback control problems of discrete-time switched systems with repeated scalar nonlinearities. Based on the switching-sequence-dependent Lyapunov functional and the positive definite diagonally dominant matrix techniques, a feasible stability solution is first proposed that not only reduces the conservativeness of the resulting closed-loop dynamic system, but also guarantees the concerned switched system is asymptotically stable with a prescribed \(\mathcal {H}_{\infty }\) disturbance attenuation performance. A desired full-order output feedback controller is also designed by introducing the projection technique and a cone complementarity linearization algorithm to convert the non-convex feasibility solution into some finite sequential minimization problems. Thus, the output feedback control parameters can be validly calculated using the standard MATLAB toolbox. Finally, the advantages and the effectiveness of the designed output feedback control technique are demonstrated by the simulation results.