Design of switched linear control systems based on Youla parameterization with average dwell time

A two-steps method of designing switched linear systems is presented with the parameterization of globally uniformly asymptotically stabilising controllers with average dwell time (ADT). First, an observer-based switching controller design is given for a class of switched linear system. Based on the construction of observer-based controller, conceptions of doubly coprime factorization and Youla parameterization of LTI systems are extended to switched linear systems with respect to globally uniformly asymptotical stability (GUAS) using a state-space expression. Second, the parameterization of closed-loop systems, which are affine with any globally uniformly asymptotically stable $ Q $ Q-parameter, is then described. This description enables the application of the $ Q $ Q –- parameter approach to a variety of switched linear control-system designs. The control construction provides us a two-steps process design procedure. Above all, based on the Schur complementary lemma and controller variable elimination method, a systematic weighted L2 performance strategy is focused on and a design scheme of $ Q $ Q to obtain weighted L2-gain performance is clarified. Finally, a numerical example is given to show the validity and potential of the developed results.