Discussions on observer design of nonlinear positive systems via T–S fuzzy modeling

Zhao, Xudong; Wu, Tingting; Zheng, Xiaolong; Li, Ren

doi:10.1016/j.neucom.2015.01.034

Cited by 43 publications

(20 citation statements)

References 10 publications

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“…While, in other papers [6], [8], [47], not only the open-loop systems is positive but also the closed-loop systems is positive. In this paper, we consider the latter case that it requires the polynomial fuzzy model (the original nonlinear plant) to be positive and the static output feedback PPFMB control system to maintain positivity and stability.…”

Section: Static Output Feedback Polynomial Fuzzy Controllermentioning

confidence: 90%

“…[1]- [4]. In recent years, positive systems have been enormously attractive to many researchers and many results have been obtained for positive linear systems such as state feedback controller design [5], positive observer and dynamic output feedback controller design [6], filter design [7] and positive nonlinear systems such as observer design [8] and filter design [9].…”

Section: Introductionmentioning

confidence: 99%

“…In [28], the stability analysis of positive interval type-2 TSK systems with application to energy markets was studied. Considering some system state variables are often unmeasurable, the work in [8] designed an observer for positive T-S fuzzy model. However, for static output feedback control, when considering the stability analysis of the closed-loop positive system, the stability conditions are usually non-convex.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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: Static Output Feedback Polynomial Fuzzy Controllermentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Static Output Feedback Stabilization of Positive Polynomial Fuzzy Systems

Meng

Lam

et al. 2018

IEEE Trans. Fuzzy Syst.

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“…Recently, nonlinear system control has attracted the attention of many scholars. At present, most control methods of nonlinear systems are mainly asymptotically stable, requiring infinite time, theoretically, to achieve the control objectives [21][22][23][24]. However, the adequacy of the steady-state performance does not represent the transient performance quality.…”

Section: Introductionmentioning

confidence: 99%

Design of a Finite-Time Terminal Sliding Mode Controller for a Nonlinear Hydro-Turbine Governing System

2020

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We focus on the finite-time control of a hydro-turbine governing system (HGS) in this paper. First, the nonlinear mathematical model of the hydro-turbine governing system is presented and is consistent with the actual project. Then, based on the finite-time stability theory and terminal sliding mode scheme, a new finite-time terminal sliding mode controller is designed for the hydro-turbine governing system and a detailed mathematical derivation is given. Only three vector controllers are required, which is less than the HGS equation dimensions and is easy to implement accordingly. Furthermore, numerical simulations for the proposed scheme and an existing sliding mode control are presented to verify the validity and advantage of improving transient performance. The approach proposed in this paper is simple and provides a reference for relevant hydropower systems.

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“…It is necessary to design observer to estimate state variables. The observer design problems for positive systems have been considered in [16][17][18][19][20]. To the best of our knowledge, the observer design for positive Markovian jump systems has not been fully investigated, especially systems with interval parameter uncertainties.…”

Section: Introductionmentioning

confidence: 99%

Positivel1State-Bounding Observer Design for Positive Interval Markovian Jump Systems

Zhang

Lyu

2016

Mathematical Problems in Engineering

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This paper studies the problem of positive 1 state-bounding observer design for a class of positive Markovian jump systems with interval parameter uncertainties by a linear programming approach. For the first, necessary and sufficient conditions are obtained for stochastic stability and 1 performance of positive Markovian jump systems by an "equivalent" deterministic positive linear system. Furthermore, based on the results obtained in this paper, sufficient conditions for the existence of the positive 1 statebounding observer are derived. The conditions can be solved in terms of linear programming. Finally, a numerical example is used to illustrate the effectiveness of the results obtained.

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Discussions on observer design of nonlinear positive systems via T–S fuzzy modeling

Cited by 43 publications

References 10 publications

Static Output Feedback Stabilization of Positive Polynomial Fuzzy Systems

Static Output Feedback Stabilization of Positive Polynomial Fuzzy Systems

Design of a Finite-Time Terminal Sliding Mode Controller for a Nonlinear Hydro-Turbine Governing System

Positivel1State-Bounding Observer Design for Positive Interval Markovian Jump Systems

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