Feedback control for switched positive linear systems

Zhang, Junfeng; Han, Zhengzhi; Zhu, Fuliang; Huang, Jun

doi:10.1049/iet-cta.2012.0428

Cited by 51 publications

(45 citation statements)

References 28 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: 89%

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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: Static Output Feedback Polynomial Fuzzy Controllermentioning

confidence: 89%

“…To study the stability of the dual PPFMB control system (9), the Lyapunov function candidate [47] is employed:…”

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

confidence: 99%

Static Output Feedback Stabilization of Positive Polynomial Fuzzy Systems

Meng

Lam

et al. 2018

IEEE Trans. Fuzzy Syst.

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“…The linear programming approach was also used to solve the routing control in networks of constrained positive systems in [29]. By technically integrating MLCLFs with linear programming, the feedback control law of SPSs was constructed in [30]. In [31], exponential stability was addressed for SPSs with stable and unstable subsystems.…”

Section: Introductionmentioning

confidence: 99%

Further results on stability and stabilisation of switched positive systems

Zhang

Huang

Zhao

2015

IET Control Theory & Applications

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This study is concerned with stability and stabilisation of switched positive systems in both continuous-and discrete-time contexts. Several criteria of Metzler/Hurwitz and non-negative/Schur matrices are presented. By using these criteria and dual system theory, a sufficient condition for stability of switched positive systems is established. On the basis of the sufficient condition, a new controller design is proposed for switched positive systems. It is shown that the proposed design reduces the conservatism of the existing approaches in the literature where the controller gain matrices always have the property of being rank one. The results are also extended to discrete-time systems. Finally, two illustrative examples verify the validity of the theoretical findings. 7

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“…Over the past decades, positive systems have been a hot topic in system theory and application. A great many of results on various topics such as positive realization [5], reachability [6,7], positivity analysis [8,9,10,11], positive stabilization [12,13,14,15], positive filter [16], have emerged.…”

Section: Introductionmentioning

confidence: 99%

“…Then, the parameter of the desired observer can be computed by(15) and is given as initial condition e 0 = 2 5 8 T , we have the response of error e(k) shown inFig. 1.…”

mentioning

confidence: 99%