control for fuzzy singularly perturbed systems

Liu, Huaping; Sun, Fuchun; Hu, Yunfeng

doi:10.1016/j.fss.2005.05.004

Cited by 63 publications

(54 citation statements)

References 39 publications

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“…In virtue of this advantage, a number of important issues in 1-D nonlinear fuzzy control systems have been well studied. Among these results, stability analysis has been studied in Jadbabaie (1999), Kim and Kim (2002), Kim and Lee (2000), systematic design procedures have been proposed in Wang et al (1996), robustness and optimality have been investigated in Liu et al (2005), Lu and Doyle (1995), Yoneyama (2006), Zhou and Li (2005), the problems of stability analysis and stabilization for a class of discrete-time T-S fuzzy systems with time-varying state delay has been studied in Wu et al (2011), the robust fault detection problem for T-S fuzzy Ito stochastic systems has been tackled in Wu and Ho (2009).…”

Section: Introductionmentioning

confidence: 99%

Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions

Chen

Lam

Gao

et al. 2011

Multidim Syst Sign Process

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This paper investigates the problem of stability analysis and stabilization for two-dimensional (2-D) discrete fuzzy systems. The 2-D fuzzy system model is established based on the Fornasini-Marchesini local state-space model, and a control design procedure is proposed based on a relaxed approach in which basis-dependent Lyapunov functions are used. First, nonquadratic stability conditions are derived by means of linear matrix inequality (LMI) technique. Then, by introducing an additional instrumental matrix variable, the stabilization problem for 2-D fuzzy systems is addressed, with LMI conditions obtained for the existence of stabilizing controllers. Finally, the effectiveness and advantages of the proposed design methods based on basis-dependent Lyapunov functions are shown via two examples.

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Section: Introductionmentioning

confidence: 99%

Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions

Chen

Lam

Gao

et al. 2011

Multidim Syst Sign Process

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“…It is important to obtain the -bound such that stability and other performances of SPSs can be ensured. Studies on -bound can be mainly divided into two types: one only presents sufficient conditions for the existence of the -bound [10,11], and the other proposes methods to estimate the -bound [9,12]. Singularly perturbed switched systems (SPSSs) consist of a group of SPSs and a certain switching law, which specifies the active SPS at the switching instance.…”

Section: Introductionmentioning

confidence: 99%

“…∞ control was addressed for fuzzy SPSs in [11,[29][30][31], and sufficient conditions independent of for the existence of ∞ controller were presented. The resulting conditions in [11,[28][29][30][31] are only applicable to stabilizing the system and being with an ∞ performance for sufficiently small . Hence, some researchers have concentrated on the -bound design problem for fuzzy SPSs [32][33][34].…”

Section: Introductionmentioning

confidence: 99%

H_∞ Control for T‐S Fuzzy Singularly Perturbed Switched Systems

Wang

Zhou

Dai

et al. 2017

Mathematical Problems in Engineering

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This paper is concerned with the design of fuzzy controller with guaranteed ∞ performance for a class of Takagi-Sugeno (T-S) fuzzy singularly perturbed switched systems. First, by using the average dwell time approach together with the piecewise Lyapunov function technique, a state feedback controller that depends on the singular perturbation parameter is developed. This controller is shown to work well for all ∈ (0, 0 ]. Then, for sufficiently small , an -independent controller design method is proposed. Furthermore, under the -independent controller, the -bound estimation problem of the overall switched closed-loop system is solved. Finally, an inverted pendulum system is used to evaluate the feasibility and effectiveness of the obtained results.

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“…On the other hand, multi-objective robust controllers can resist disturbance and guarantee dynamic performance at the same time, which is well suited for flight control. Previous work such as [8][9][10][11][12][13][14] dealt with the robust control problem of FSPM with parameter perturbation. However, they only focused on a single perturbation parameter.…”

Section: Introductionmentioning

confidence: 99%

Multi-objective robust control based on fuzzy singularly perturbed models for hypersonic vehicles

Yuan

Min

et al. 2011

Sci. China Inf. Sci.

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In this paper, we propose a multi-objective robust controller based on fuzzy singularly perturbed models (FSPM) for the longitudinal motion of an air-breathing hypersonic vehicle. The control objective is to provide velocity and altitude tracking in the presence of the uncertainties and unknown nonlinearities in the model caused by variations in flight conditions. By approximating the multi-time-scale model with FSPM, ill-posed matrix calculations are circumvented. Under this framework, a fuzzy multi-objective robust controller is developed, and the linear matrix inequalities (LMI) condition is derived. Numerical simulation using the longitudinal model of a hypersonic aircraft is provided to demonstrate the effectiveness of the proposed strategy. CitationHu Y N, Yuan Y, Min H B, et al. Multi-objective robust control based on fuzzy singularly perturbed models for hypersonic vehicles.

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control for fuzzy singularly perturbed systems

Cited by 63 publications

References 39 publications

Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions

Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions

H_∞ Control for T‐S Fuzzy Singularly Perturbed Switched Systems

Multi-objective robust control based on fuzzy singularly perturbed models for hypersonic vehicles

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control for fuzzy singularly perturbed systems

Cited by 63 publications

References 39 publications

Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions

Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions

H∞ Control for T‐S Fuzzy Singularly Perturbed Switched Systems

Multi-objective robust control based on fuzzy singularly perturbed models for hypersonic vehicles

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H_∞ Control for T‐S Fuzzy Singularly Perturbed Switched Systems