ABSTRACT
This article investigates the problems of invariant set analysis and control synthesis for switched singular systems where the subsystems exhibit distinct equilibria. Considering equilibrium shifts and algebraic constraints, the state jump behaviors at switching instants are formulated, transforming the original system equivalently into a reduced-order multi-equilibrium switched system with state jumps. By introducing equilibrium-related Lyapunov functions, invariant set criteria for the reduced-order system are derived, ensuring the invariant set property of the original system. Furthermore, a guaranteed cost multi-equilibrium switched singular (GC-MESS) controller is designed, which not only guarantees the invariant set of the closed-loop original system but also achieves the one-period guaranteed cost. Compared to previous studies on switched singular systems, this work represents the first attempt to address the multi-equilibrium characteristic. A numerical example and an application example are provided to demonstrate the effectiveness and potential of the proposed theoretical results.
International Journal of Robust and Nonlinear Control, Volume 35, Issue 18, Page 7485-7498, December 2025. Read More
