Invariant Set Analysis and Control Synthesis of Multi-Equilibrium Switched Systems under Control Constraints

This paper investigates the problems of invariant set analysis and control synthesis for multi-equilibrium switched systems under control constraints. A control strategy based on the invariant set method is proposed, accompanied by criteria formulated as linear matrix inequalities, ensuring that the state remains within the mode-dependent invariant sets. Furthermore, considering the control constraints in practical scenarios, a multi-equilibrium switched controller with control constraints (MESCC controller) is designed. Compared to existing works, the proposed method incorporates mode-dependent dwell time conditions and mode-dependent invariant sets, thereby offering enhanced design flexibility. An example of an aero-engine control system is presented to demonstrate the effectiveness and potential of the theoretical results.