Using modal analysis to guarantee the closed loop behaviour of a class of hybrid systems

Several issues in the control of a class of hybrid systems are discussed. The class of hybrid systems considered are linear time-varying plants controlled by means of switching between homogeneous controllers. In this paper modal analysis is used to analyse the behaviour of switching systems with real eigensystems. Conditions guaranteeing the stability of such systems are presented and guidelines for shaping their transient response given. It is demonstrated that for SISO systems, controlled by means of dynamic state feedback, a local state approach can be employed which results in a closed loop system with guaranteed asymptotic stability irrespective of switching frequency. The theory presented is used in the design of a hybrid speed control system for a real automobile which guaranteed nominal stability and good transient response properties.