Stability analysis and stabilization for fuzzy hyperbolic time-delay system based on delay partitioning approach

This paper investigates the problems of stability analysis and stabilization for a class of fuzzy hyperbolic time-delay systems. A generalization of the fuzzy hyperbolic time-delay model is firstly proposed, which is more effective in representing nonlinear control systems. By means of the delay-partitioning method, a novel basis-dependent Lyapunov-Krasovskii function is constructed to reduce the conservatism of stability conditions. Those conditions are converted to finite linear matrix inequalities, which can be readily solved by standard numerical software. Using this result, the problem of stabilization is also solved. Then, both the stability and stabilization results are further extended to fuzzy hyperbolic time-delay systems with parameter uncertainties. Finally, three illustrative examples are provided to demonstrate the feasibility and effectiveness of the proposed methods.