Asynchronous Switching Control for Fuzzy Markov Jump Systems With Periodically Varying Delay and Its Application to Electronic Circuits

This article focuses on addressing the issue of asynchronous
${H_\infty}$
control for Takagi-Sugeno (T-S) fuzzy Markov jump systems with generally incomplete transition probabilities (TPs). The delay is assumed to vary periodically, resulting in one monotonically increasing interval and one monotonically decreasing interval during each period. Meanwhile, a new Lyapunov-Krasovskii functional (LKF) is devised, which depends on membership functions (MFs) and two looped functions formulated for the monotonic intervals. Since the modes and TPs of the original system are assumed to be unavailable, an asynchronous switching fuzzy controller on the basis of hidden Markov model is proposed to stabilize the fuzzy Markov jump systems (FMJSs) with generally incomplete TPs. Consequently, a stability criterion with improved practicality and reduced conservatism is derived, ensuring the stochastic stability and
${H_\infty}$
performance of the closed-loop system. Finally, this technique is employed to the tunnel diode circuit system, and a comparison example is given, which verifies the practicality and superiority of the method.
Note to Practitioners
—As a category of stochastic hybrid nonlinear systems driven by continuous time and discrete events, FMJSs have significant applications in practical engineering such as aircraft control systems and large-scale manufacturing systems. However, the real-time acquisition of system mode information and TPs is difficult due to technological constraints and limited resources. Moreover, the presence of periodically varying delay is prevalent in many industrial processes, resulting in degradation of dynamic system performance and instability. Therefore, it is necessary to study the FMJSs with generally incomplete TPs and periodically varying delays in asynchronous framework. Accordingly, unlike previous work, the designed LKF relies on system modes, MFs, and two looped functions for monotonic intervals. This new LKF exhibits a high degree of flexibility, fully leveraging the information of MFs and periodically varying delays, which can significantly reduce conservatism.