Finite-time stabilization of switched nonlinear systems with partial unstable modes

This paper investigates the finite-time stabilization problem of switched nonlinear systems (SNS) in the presence of impulse effects, where both stable subsystems and unstable subsystems coexist. A new notion named mode-dependent average switching frequency (MDASF) is firstly proposed by extending the previous average switching frequency method (ASF). Designing mode-dependent switching law reveals the tradeoff among stable and unstable modes. Based on the estimation on transition matrix and Gronwall–Bellman inequality, mode-dependent feedback controllers are constructed to achieve finite-time stability of the closed-loop systems. Finally, a numerical example is given to verify the efficiency of the proposed method and the validity of our results.