Local stability analysis of continuous-time Takagi–Sugeno fuzzy systems: A fuzzy Lyapunov function approach

Lee, Dong Hwan; Joo, Young Hoon; Tak, Myung Hwan

doi:10.1016/j.ins.2013.08.036

Cited by 78 publications

(23 citation statements)

References 54 publications

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“…Remark 4: Based on the nonsingular transformation matrix Γ, we can obtain convex stability conditions (18) and positivity conditions (20) which are linear in the decision variables h and Z j (y). Once there exist feasible h and Z j (y), λ can be obtained by (15) and the polynomial feedback gains K j (y) can be obtained by (16).…”

Section: A Basic Stability Analysis Of Static Output Feedback Ppfmb mentioning

confidence: 99%

“…Remark 5: The positivity condition (21) is used to ensure the matrix A i (x) + B i (x)K j (y)C to be a Metzler matrix for all i and j according to (20). The stability condition (22) is used to ensure V (t) > 0 (excluding x = 0) by meeting λ 0.…”

Section: A Basic Stability Analysis Of Static Output Feedback Ppfmb mentioning

confidence: 99%

“…For discrete-time single-input singleoutput (SISO) systems, the work in [19] investigated the stable and convergent iterative feedback tuning of fuzzy controllers. Based on the fuzzy Lyapunov function approach, the paper [20] discussed the local stability analysis of continuous-time T-S fuzzy systems. Some work in [21]- [24] investigated adaptive output feedback fuzzy control methods.…”

Section: Introductionmentioning

confidence: 99%

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Static Output Feedback Stabilization of Positive Polynomial Fuzzy Systems

Meng

Lam

et al. 2018

IEEE Trans. Fuzzy Syst.

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Abstract-This paper deals with the static output feedback stabilization of positive polynomial fuzzy-model-based (PPFMB) control systems. The positive polynomial fuzzy model does not need to share the same premise membership functions with the static output feedback polynomial fuzzy controller. Unlike the state feedback control case, the static output feedback control usually leads to non-convex stability conditions. To circumvent the problem, an approach is employed to transform the nonconvex stability conditions into convex ones by introducing a nonsingular transformation matrix. Initially, the conditions guaranteeing the resultant closed-loop systems to be positive and asymptotically stable are obtained. Moreover, the divisional approximated membership functions which carry the local information of the membership functions are employed to facilitate the stability analysis and controller synthesis. The relaxed stability conditions in terms of sum of squares (SOS) are obtained based on Lyapunov stability theory. Finally, a simulation example is given to testify the validity of the analysis result.

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Section: A Basic Stability Analysis Of Static Output Feedback Ppfmb mentioning

confidence: 99%

Section: A Basic Stability Analysis Of Static Output Feedback Ppfmb mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Static Output Feedback Stabilization of Positive Polynomial Fuzzy Systems

Meng

Lam

et al. 2018

IEEE Trans. Fuzzy Syst.

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“…Hence, Takagi-Sugeno fuzzy model has been used in analyzing nonlinear systems and designing stabilizing controllers. The stability of fuzzy systems was investigated in [2], [3], and [4]. Unfortunately, however, the recent paper [4] gave novel stability conditions but no control design method was provided there.…”

Section: Introductionmentioning

confidence: 99%

Non-Fragile Dynamic Output Feedback Control Design for Fuzzy Stochastic Systems

Yoneyama

Hoshino

2016

Transactions of ISCIE

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The paper considers a non-fagile control design via dynamic output feedback controller for fuzzy stochastic systems that are subject to stochastic disturbances. In practical situations, robust control design methods should take case of disturbances into the system and variations in control gains, and they should assume that not all the states of the system are available for the feedback control. In addition, malfunction may occur in actuators. Hence, a non-fragile output feedback control design is desired. In this paper, robust stabilization via dynamic output feedback control with uncertain control gain for fuzzy stochastic systems is considered and a control design of robust stabilizing controllers is proposed. The robust stability analysis of the closed-loop system and non-fragile controller design via descriptor system approach are given in terms of LMI conditions. The resulting conditions are less conservative than the existing results. An illustrative example is provided to show the effectiveness of the proposed method.

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“…While for LTI systems, the exact DT model is available in principle, this is not the case for nonlinear systems [15,16] or uncertain LTI systems [3,17]. Rather, an approximate DT model can be used in replacement of the exact DT model for the SD control design.…”

Section: Introductionmentioning

confidence: 99%

Robust Discretization of LTI Systems with Polytopic Uncertainties and Aperiodic Sampling

Lee

Park²,

Joo

2015

Journal of Electrical Engineering and Technology

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-In the previous work, the authors studied the problem of robust discretization of linear time-invariant systems with polytopic uncertainties, where linear matrix inequality (LMI) conditions were developed to find an approximate discrete-time (DT) model of a continuous-time (CT) system with uncertainties in polytopic domain. The system matrices of obtained DT model preserved the polytopic structures of the original CT system. In this paper, we extend the previous approach to solve the problem of robust discretization of polytopic uncertain systems with aperiodic sampling. In contrast with the previous work, the sampling period is assumed to be unknown, time-varying, but contained within a known interval. The solution procedures are presented in terms of unidimensional optimizations subject to LMI constraints which are numerically tractable via LMI solvers. Finally, an example is given to show the validity of the proposed techniques.

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Local stability analysis of continuous-time Takagi–Sugeno fuzzy systems: A fuzzy Lyapunov function approach

Cited by 78 publications

References 54 publications

Static Output Feedback Stabilization of Positive Polynomial Fuzzy Systems

Static Output Feedback Stabilization of Positive Polynomial Fuzzy Systems

Non-Fragile Dynamic Output Feedback Control Design for Fuzzy Stochastic Systems

Robust Discretization of LTI Systems with Polytopic Uncertainties and Aperiodic Sampling

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