Contents I. Introduction
Switched systems are encountered in various industrial applications (mechanics, automotive, aircraft and air traffic, switching power converters, etc.), hence the control design for such systems has become an important research topic. Switched systems belong to a special class of hybrid systems consisting of several subsystems described by linear dynamics together with a switching rule defining the active subsystem in each time instant. The most important control objective is to guarantee stability closed-loop stability of individual subsystems and stability during arbitrary switching between them. A considerable research effort devoted to this issue can be found in [1], [2], [3], [4]. Majority of existing approaches to control design for switched linear systems are based on time-domain state-space analysis leading to state or static output feedback or high order dynamic feedback controllers [5], [6]. If the switching signal is not a design variable but belongs to a prescribed admissible set, the problem reduces to finding a feedback control law which ensures closed-loop stability under any switching signal. This problem is closely related to the robust control problem of polytopic uncertain linear systems addressable by the Lyapunov approach. However, in this way the robust controller design leads to Bilinear Matrix Inequalities (BMI) [7]. Conservatism of these approaches can be reduced using switched Lyapunov function approach that leads to static output feedback design [6]. On the other hand, very little work regarding frequency domain design approaches can be found in the literature.
