Stabilization of Singularly Perturbed Fuzzy Systems

Abstract

This paper presents some novel results for stabilizing singularly perturbed (SP) nonlinear systems with guaranteed control performance. By using Takagi-Sugeno fuzzy model, we construct the SP fuzzy (SPF) systems. The corresponding fuzzy slow and fast subsystems of the original SPF system are also obtained. Two fuzzy control designs are explored. In the first design method, we propose the composite fuzzy control to stabilize the SPF subsystem with control performance. Based on the Lyapunov stability theorem, the stability conditions are reduced to the linear matrix inequality (LMI) problem. The composite fuzzy control will stabilize the original SP nonlinear systems for all (0 ) and the upper bound can be determined. For the second design method, we present a direct fuzzy control scheme to stabilize the SP nonlinear system with control performance. By utilizing the Lyapunov stability theorem, the direct fuzzy control can guarantee the stability of the original SP nonlinear systems for a given interval [ ]. The stability conditions are also expressed in the LMIs. Two SP nonlinear systems are adopted to demonstrate the feasibility and effectiveness of the proposed control schemes. Index Terms-control performance, linear matrix inequality (LMI), singularly perturbed fuzzy (SPF) systems, singularly perturbed (SP) nonlinear systems, Takagi-Sugeno (T-S) fuzzy model.

The direct adaptive control based on the singularly perturbed model with the unknown consequence parameters

“…Theorem 1: Given the plant (1), (2) and stable reference model (6), (7), the control law (12) and adaptive law (21), (22) are applied, suppose reference signal r(t) and reference stable variable vector x m (t) are consistently bounded, we have ( ) t → e 0 when t → ∞ with bounded control law and actual state vector.…”

“…The ε -depended LMIs will be convergent to zero if ε is near zero. While in [12] fuzzy subsystems are decomposed into fast and slow subsystems and the sub-H ∞ controllers were designed, respectively, and then composes the final controller. The stable upper bound of perturbed parameters * ε can be achieved by computation.…”

control for fuzzy singularly perturbed systems

“…Very recently, there has appeared some researches on control of fuzzy singularly perturbed systems [2,20,22], but no static output feedback control was investigated in those literatures.…”

MIMO adaptive fuzzy terminal sliding-mode controller for robotic manipulators

“…However, chattering is a drawback of the sliding-mode control. While fuzzy logic has been applied to nonlinear systems with uncertainties [1,2,9,13,19,21,22,[26][27][28][29]35,36,38,42,43,47,50,51], the large number of fuzzy rules makes the design complex.…”