H ∞ Control of T-S Fuzzy Singularly Perturbed Systems Using Multiple Lyapunov Functions

Asemani, Mohammad Hassan; Yazdanpanah, Mohammad Javad; Majd, Vahid Johari; Golabi, Arash

doi:10.1007/s00034-013-9562-y

Cited by 15 publications

(4 citation statements)

References 35 publications

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“…Summarize the results of DOFC in recent years. 20,22,[25][26][27][28] Reference 25 compared with Reference 20, the former gives an inequality algorithm to determine the boundary and avoids the trouble caused by the trial value in the latter. Reference 26 considers the robust control for the linear singularly perturbed system by the approach in Reference 19, but there is no in-depth research on nonlinear SPSs.…”

Section: Introductionmentioning

confidence: 99%

“…However, this controller contains weighting constants needed to be chosen subjectively, leading to conservatism and inconvenience in practice to same extent. Summarize the results of DOFC in recent years 20,22,25–28 . Reference 25 compared with Reference 20, the former gives an inequality algorithm to determine the boundary and avoids the trouble caused by the trial value in the latter.…”

Section: Introductionmentioning

confidence: 99%

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Robust multiobjective control of singularly perturbed systems using linear matrix inequality

Wang

2022

Adaptive Control & Signal

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The article investigates the issue of designing H ∞ output feedback controller for a fuzzy nonlinear singularly perturbed systems (SPSs). From overall perspective, we design a series of linear matrix inequalities conditions, which provides the optional stability bounds ℇ 0 , verifies the existence of ℇ 0 and ensures that the T-S fuzzy SPSs are asymptotic stable for all ℇ ∈ (0, ℇ 0 ]. According to the characteristics of SPSs, we design the asymmetric auxiliary matrix P(ℇ), which reduces the conservatism and expands the application scope of ℇ in contrast to the previous results. The approach gives the ℇ-dependent Lyapunov function and deduces the fuzzy ℇ-dependent robust controller. It is not only can be applied to the standard or nonstandard nonlinear systems but also eliminates the ill-conditioned problems. Finally, a numerical example testifies the feasibility of conclusion.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust multiobjective control of singularly perturbed systems using linear matrix inequality

Wang

2022

Adaptive Control & Signal

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“…Several studies have used the NQLF [12,[16][17][18][19]. At first, NQLF-based approaches lead to bilinear matrix inequality (BMI) conditions, which can be conservative and non-convex [20].…”

Section: Introductionmentioning

confidence: 99%

“…Several studies are concerned with reducing the conservatism of the stability conditions. For instant, introducing some slack matrices by means of closed‐loop system properties , utilizing some decoupling lemmas , or Finsler's lemma , using descriptor form instead of state space representation , and expanding the degree of fuzzy summations .…”

Section: Introductionmentioning

confidence: 99%

More Relaxed Non‐Quadratic Stabilization Conditions Using Ts Open Loop System and Control Law Properties

Vafamand

Shasadeghi

2016

Asian Journal of Control

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This paper proposes more relaxed stabilization conditions based on a non‐quadratic Lyapunov function (NQLF) and parallel distributed compensator (PDC) controller. The conditions are derived in terms of linear matrix inequalities (LMIs) by introducing three slack matrices based on the properties of TS membership functions, an open loop system and a PDC controller. These slack matrices are utilized to decouple the LMI variables from the TS system and the input matrices. Therefore, the proposed approach greatly reduces the number of LMI conditions and improves feasibility by providing more degrees of freedom compared to recently published studies. Moreover, local stability and stabilization conditions are considered to handle the time derivatives of membership functions appearing in the stabilization synthesis of the TS closed‐loop system with PDC controller. Finally, several examples are presented to demonstrate the advantages of the proposed approaches.

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$$H_\infty $$ H ∞ Control and $$\varepsilon $$ ε -Bound Estimation of Discrete-Time Singularly Perturbed Systems

Yang

Zhou

2015

Circuits Syst Signal Process

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H ∞ Control of T-S Fuzzy Singularly Perturbed Systems Using Multiple Lyapunov Functions

Cited by 15 publications

References 35 publications

Robust multiobjective control of singularly perturbed systems using linear matrix inequality

Robust multiobjective control of singularly perturbed systems using linear matrix inequality

More Relaxed Non‐Quadratic Stabilization Conditions Using Ts Open Loop System and Control Law Properties

$$H_\infty $$ H ∞ Control and $$\varepsilon $$ ε -Bound Estimation of Discrete-Time Singularly Perturbed Systems

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