Control Synthesis of Multi‐Equilibrium Asynchronously Switched Systems Under Control Constraints

ABSTRACT This paper investigates the problems of invariant set analysis and control synthesis for asynchronously switched systems where the subsystems exhibit distinct equilibria. The general case of asynchronous switching is examined for the first time within the context of multi‐equilibrium switched systems. By analyzing multiple Lyapunov functions related to the equilibria, an asynchronous control strategy is proposed to ensure that the state remains within the mode‐dependent invariant set, based on which numerically testable invariant set criteria are derived. Furthermore, a multi‐equilibrium switched controller with control constraints (MESCC controller) is designed, which not only ensures the invariant set property of the closed‐loop systems but also effectively limits the magnitude and rate of change of the control signals. Compared to previous studies on multi‐equilibrium switched systems, this paper extends the existing results from invariant set analysis to controller design, while also addressing the asynchronous phenomenon and control constraints in practical scenarios. An illustrative example of the F‐18 flight control system is provided to demonstrate the effectiveness and potential of the theoretical results.