Finite‐Time Stability Analysis of T‐S Fuzzy Systems With State‐Dependent Delayed Impulses

ABSTRACT

In this work, finite‐time stability (FTS) is examined for a class of Takagi–Sugeno (T‐S) fuzzy systems that involve both time‐delay and state‐dependent delayed (SDD) impulses. For the first time the SDD impulses ) is introduced in the T‐S fuzzy system to analyze the system dynamics in the presence of SDD. Also, the time‐dependent and impulse‐dependent Lyapunov‐Krasovskii functional is introduced to derive the FTS conditions based on linear matrix inequality. Some sufficient conditions of FTS for T‐S fuzzy delayed systems are obtained by designing a delayed state feedback control and SDD impulses. The FTS conditions are derived by considering the upper bound of both the impulsive interval and the time‐delay is one more novelty of this work. Finally, the theoretical results effectiveness are demonstrated in applying the Rossler and Lorenz systems.