Improved stability criteria of T-S fuzzy systems with sampled-data-based dissipative control

Highlights：

• Some of the terms in the Lyapunov functional need not to be positive definite, owing to the improved LKF approach. Some of the elements of this function can be negative definite over the sample interval, weakening some LKF requirements. Less conservative dissipative stability conditions of the T-S fuzzy system are obtained. Moreover, the output-feedback controller gain can be also derived.

• By using relaxed Free-matrix-based (FMB) integral inequality and reciprocally convex method, a series of new stability conditions were expressed as linear matrix inequalities to ensure the stability of system.

摘要

•This work studies dissipative control for Takagi-Sugeno (T-S) fuzzy sampling system. The fuzzy model of nonlinear systems with disturbance is considered and an improved output-feedback control strategy is proposed. The T-S fuzzy model combined with the fuzzy membership functions (FMFS) are considered which derive the less conservative result. A novel two-sided Lyapunov looped-functional will be constructed. This functional is dependent on the FMFs, so as to reduce the conservativeness. What more, the less conservative stability criterions are derived by means of some novel integral inequalities.•Some of the terms in the Lyapunov functional need not to be positive definite, owing to the improved LKF approach. Some of the elements of this function can be negative definite over the sample interval, weakening some LKF requirements. Less conservative dissipative stability conditions of the T-S fuzzy system are obtained. Moreover, the output-feedback controller gain can be also derived.•By using relaxed Free-matrix-based (FMB) integral inequality and reciprocally convex method, a series of new stability conditions were expressed as linear matrix inequalities to ensure the stability of system.