Stability analysis and L₂-gain control for positive fuzzy systems by applying a membership-function-dependent Lyapunov function

Stability and L-2-gain control for positive Takagi-Sugeno (T-S) fuzzy systems are further studied in this brief paper. First, considering that the system states are positive, some sufficient conditions of exponential asymptotic stability are obtained by applying a copositive Lyapunov function with membership-function-dependent (MFD) Lyapunov matrices. Based on a preset switching rule, the conditions are expressed as linear matrix inequalities by eliminating the nonconvex factors due to the time derivative of MFD Lyapunov matrices. Then, stability is extended to stabilization by designing a switching controller with time-varying controller gains such that the L-2-gain performance requirements are satisfied. In addition, a quadratic switching strategy is established to further reduce conservativeness. Finally, the applicability and validity of the theoretical results are validated by two examples.