Stability analysis and L2-gain of nonlinear switched systems with unstable subsystems

For a class of discrete-time nonlinear switched systems which contains stable and unstable subsystems, the issue for stability analysis and L
₂
-gain is studied. The Takagi and Sugeno (T-S) fuzzy model is adopted to represent each subsystem. By this means, the class of discrete-time nonlinear switched systems are modeled into the discrete-time switched T-S fuzzy systems. The mode-dependent average dwell time (MDADT) approach and switching fuzzy-basis-dependent Lyapunov functions (FLFs) technique are employed to investigate the discrete-time switched T-S fuzzy systems. New sufficient conditions are derived, which guarantee the stability and weighted ¿2-gain of discrete-time switched T-S fuzzy systems with stable and unstable subsystems. All these conditions can be represented by linear matrix inequalities. At last, the effectiveness of the obtained conditions is illustrated by a numerical example.