Finite‐time stability analysis of a class of discrete‐time switched nonlinear systems with partial finite‐time unstable modes

Plenty of research achievements on finite-time stability of discrete-time switched systems have been reported; however, there are a few results referred to finite-time unstable subsystems. The design of the average dwell time was not considered alone for finite-time unstable subsystems in the existing literature. The problems of finite-time stability and finite-time boundedness are investigated respectively for a class of discrete-time switched nonlinear systems with partial finite-time unstable modes. By using multiple Lyapunov-like functions, sufficient conditions are derived respectively to ensure that such systems are finite-time stable and finite-time bounded based on an improved mode-dependent average dwell time and iteration technique. Depending on the above results, sufficient conditions, which can guarantee discrete-time switched linear systems finite-time stable and finite-time bounded, are obtained respectively by using matrix inequalities. Finally, numerical examples are given to verify the effectiveness of the proposed methods.