Upper Bound Of Singular Perturbation Parameter Research Articles

Asynchronous Control of Fuzzy Singularly Perturbed System With a Dynamic Event-Triggered Strategy

This paper is mainly concerned with the asynchronous control problem of fuzzy singularly perturbed systems (FSPSs) by designing an effective dynamic event-triggered control (ETC) strategy. Different from the existing results, a sample-based dynamic eventtriggering condition related to the singular perturbation parameter (SPP) " is proposed. Particularly, an auxiliary variable is employed in the eventtriggered mechanism (ETM), which changes with the fluctuation of the system state. By constructing a novel parameter-dependent Lyapunov functional, some sufficient conditions are derived to stabilize FSPSs and solve the "-dependent control gain. Furthermore, the upper bound of SPP _" related with the proposed control gain is determined. The Zeno behavior can be naturally avoided by applying the sample-based dynamic ETC. Finally, two examples including a nonlinear circuit are presented to validate the effectiveness of obtained results.

On Output Feedback Multiobjective Control for Singularly Perturbed Systems

A new design procedure for a robust H2 and H∞ control of continuous‐time singularly perturbed systems via dynamic output feedback is presented. By formulating all objectives in terms of a common Lyapunov function, the controller will be designed through solving a set of inequalities. Therefore, a dynamic output feedback controller is developed such that H∞ and H2 performance of the resulting closed‐loop system is less than or equal to some prescribed value. Also, H∞ and H2 performance for a given upperbound of singular perturbation parameter ε ∈ (0, ε∗] are guaranteed. It is shown that the ε‐dependent controller is well defined for any ε ∈ (0, ε∗] and can be reduced to an ε‐independent one so long as ε is sufficiently small. Finally, numerical simulations are provided to validate the proposed controller. Numerical simulations coincide with the theoretical analysis.