Stability and <inline-formula> <tex-math notation="LaTeX">$\boldsymbol{L_{1}}$</tex-math> </inline-formula> -Gain Analysis for Positive Takagi–Sugeno Fuzzy Systems With Impulse

Abstract

This paper is concerned with the stability analysis and $L_{1}$ -gain characterization for positive Takagi–Sugeno fuzzy systems subject to impulse effects. The main tool utilized is the construction of an impulse-time-dependent discretized copositive Lyapunov function where the impulse interval partitioning idea is exploited to derive less conservative results. For the disturbance-free case, stability criteria are developed to guarantee global exponential stability of the concerned systems under ranged and constant dwell-time constraints. The analysis of the influence of the discretizing parameter on the reduction of conservativeness is performed. We further employ the proposed impulse-time-dependent discretized copositive Lyapunov function to analyze the $L_{1}$ -gain performance for the case where external disturbances are considered. By performing a grid search for a scalar in an interval, all the proposed criteria can be checked via linear programming. Finally, numerical simulations are discussed to illustrate the effectiveness of the theoretical results.