New results on static output feedback H_∞ control for fuzzy singularly perturbed systems: a linear matrix inequality approach

Abstract

SUMMARYThis paper presents the novel approaches of designing robust fuzzy static output feedback H ∞ controller for a class of nonlinear singularly perturbed systems. Specifically, the considered system is approximated by a fuzzy singularly perturbed model. With the use of linear matrix inequality (LMI) methods, two methods are provided to design fuzzy static output feedback H ∞ controllers. The resulted controllers can guarantee that the closed‐loop systems are asymptotically stable and satisfy H ∞ performances for sufficiently small ϵ. In contrast to the existing results, the proposed approaches have two advantages: (i) the gains of controller are solved directly by a set of ϵ‐independent LMIs, and therefore, the problem of selecting the initial values in iterative LMIs algorithm can be avoided, and (ii) the smaller control input efforts are needed. The given methods are easy to implement and can be applied to both standard and nonstandard nonlinear singularly perturbed systems. Two numerical examples are provided to illustrate the effectiveness of the developed methods. Copyright © 2012 John Wiley & Sons, Ltd.

Dynamic output feedback controller design for interval type‐2 T–S fuzzy fractional order systems

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Observer‐based event‐triggered control for singularly perturbed systems with saturating actuator

“…During system analysis and design, the interaction between fast and slow modes brings about ill‐conditioned numerical (ICN) and high‐dimensionality issues. Such multi–time‐scale models are described as singularly perturbed systems (SPSs), which contain a singular perturbation parameter (SPP) ε . One of the main problems for SPSs is to find the ε ‐bound ε 0 , such that the performance of SPSs is guaranteed for ∀ ε ∈ (0, ε 0 ] .…”

“…Such multi-time-scale models are described as singularly perturbed systems (SPSs), which contain a singular perturbation parameter (SPP) . [1][2][3][4] One of the main problems for SPSs is to find the -bound 0 , such that the performance of SPSs is guaranteed for ∀ ∈ (0, 0 ]. 3,4 The issues of controller design and estimating the -bound for SPSs have been considered, which are illustrated by electronic circuits systems.…”

“…[1][2][3][4] One of the main problems for SPSs is to find the -bound 0 , such that the performance of SPSs is guaranteed for ∀ ∈ (0, 0 ]. 3,4 The issues of controller design and estimating the -bound for SPSs have been considered, which are illustrated by electronic circuits systems. 5,6 Considering the application range of the system, studying the problems of estimating the -bound for SPSs with saturation factor attracts our attention, which is a complex and challenging topic.…”

Robust stabilization for standard discrete-time fuzzy singularly perturbed systems: A spectral norm approach

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