Asynchronous Observer Design for Fuzzy Control of Nonlinear Semi-Markov Jump Singularly Perturbed Systems

This article provides a novel framework for the concurrent development of asynchronous observers and controllers for discrete-time nonlinear semi-Markov jump singularly perturbed systems subjected to mismatched modes, states, and premise variables between controlled systems and observer-based controllers. Aiming at characterizing nonlinearity with parameter uncertainty, the interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy technique is implemented in system modeling. Meanwhile, it is supposed that both observer and controller modes can just be acquired via a hidden Markov mode detector in the first attempt. Then, following the concept of non-parallel distribution compensation (non-PDC), the observer-based IT2 fuzzy asynchronous controllers are constructed with observers and controllers sharing the same fuzzy membership function but different from that in systems, which improves the designed flexibility. In accordance with semi-Markov kernel approach and the Lyapunov function contingent upon both system modes and sojourn times, sufficient criteria are established for the functioning of expected mode-dependent IT2 fuzzy observers and controllers such that the σ-mean-square stability for the resulting nonlinear augmented semi-Markov jump singularly perturbed systems comprised of the controlled systems and observation error systems is guaranteed. Furthermore, from the perspective of fuzzy processing, parameters and relaxation matrices that comply with fuzzy rules are added to ensure system stability while further reducing the conservatism of conditions. Ultimately, a circuit model and comparison examples are shown to substantiate the necessity and superiority of the suggested technique.