Toward unified analysis and controller synthesis for a class of hybrid systems

This work defines a new class of hybrid systems called state-based switched (SBS) systems that have numerous important engineering applications. The characterizing feature of these systems is that the discrete-event dynamics are associated with the continuous-time state making a specific function be equal to zero. The choice of this function is application specific and for the closed-loop SBS systems defined in this paper it is related to the execution of a desired set of tasks from a pre-specified mission plan. For this broad class of SBS systems, the paper presents a unified analysis and controller synthesis methodology based on Lyapunov theory. Depending on the details of the mission plan, the closed-loop hybrid system will be divided into two subclasses: sequential and non-sequential. The controller design procedure for both subclasses consists of the same two steps: finding a control law and finding a stabilizing switching rule. For static state and output feedback of sequential hybrid systems, the paper proposes a new hybrid sequential sliding-mode controller. It is proven that the control mission can be accomplished for sequential hybrid systems under static state and output feedback using this new controller. A similar framework is investigated for the more complex class of nonsequential hybrid systems and a systematic procedure for designing the switching rule is presented for some specific instances of these systems.