Stability and Stabilization of Fuzzy Singular Hybrid Systems With State Jumps and Asynchronous Switching

This paper investigates the stability analysis and control synthesis for a class of continuous-time fuzzy singular hybrid systems with state jumps and asynchronous switching, motivated by practical control challenges arising in Hybrid Terrestrial and Aerial Quadrotors (HyTAQs). A Lyapunov function associated with the controller mode, rather than the plant mode, is introduced into singular hybrid systems for the first time. Compared with the plant-mode-dependent Lyapunov functions commonly adopted in existing studies, the proposed function not only facilitates stability analysis during asynchronous intervals, but also reduces conservatism in controller design. In addition, a Takagi–Sugeno (T-S) fuzzy model is employed to capture the nonlinear dynamics of practical systems accurately. Numerically testable stability criteria are established, based on which the existence conditions for fuzzy switched controllers are derived. Illustrative examples, including HyTAQs, are provided to validate the effectiveness and applicability of the developed theoretical results.