Stabilisability and observer-based switched control design for switched linear systems

Output stabilisability and observer-based switched control design problems for systems that switch among a finite set of controllable and observable linear subsystems at any given switching frequency are studied. First, the fact that output stabilisability and the observability of each subsystem can guarantee the asymptotical stabilisability of switched systems can be proved. Then, on the basis of some lemmas and much more mathematical knowledge, such as Minkowski´s integral inequality, Young´s inequality, convolution and so on, a method to design an observer-based switched control is presented that guarantees the asymptotic stabilisability of switched systems at any given switching frequency less than a given bound. Finally, an example to illustrate the obtained results is given.