Intelligent Sliding Mode Control for Fuzzy Time-Delay Systems with Periodic Impulse

This paper delves into the application of integral sliding mode control (ISMC) in addressing the complexities of fuzzy time-delay systems with periodic impulses. Unlike the sliding mode control method for continuous systems, the design of ISMC for impulsive hybrid systems is much more difficult due to the presence of pulses, especially to ensure the continuity of the sliding mode surface. Initially, a sophisticated fuzzy sliding mode surface is introduced, accompanied by a purposefully crafted fuzzy ISMC scheme incorporating impulsive signals. Subsequently, by employing a piecewise time-dependent Lyapunov function, we establish the globally asymptotic stability of the closed-loop system. To enhance practical applicability, a control design algorithm is devised, determining optimal control and feedback gains. This algorithm, rooted in derived sufficient conditions and guided by linear matrix inequality (LMI) theory, ensures a systematic parameter selection process. The culmination lies in a compelling simulation example, vividly illustrating the effectiveness of the proposed fuzzy ISMC scheme in real-world scenarios.