Observers for linear positive systems

Härdin, Hanna M.; Schuppen, Jan van

doi:10.1016/j.laa.2007.03.007

Cited by 65 publications

(46 citation statements)

References 23 publications

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“…Remark 8 From Theorem 1, it can be seen that a smaller α and a larger β will be favorable to the feasibility of (7,8). For given positive constants α and β, if (7,8) have no feasible solution, we can adjust the parameter α to be smaller or the parameter β to be larger.…”

Section: Remark 7 Compared With the Existing Results In The Literaturesmentioning

confidence: 99%

“…For given positive constants α and β, if (7,8) have no feasible solution, we can adjust the parameter α to be smaller or the parameter β to be larger. Following this guideline, a solution to (7,8) can be found. We now present the following algorithm for constructing the positive L 1 observer.…”

Section: Remark 7 Compared With the Existing Results In The Literaturesmentioning

confidence: 99%

“…To ensure the stability of error switched system (4), the error subsystem p with unobservable pair (A p , C p ) is allowed to be unstable with bounded growth. Conditions (8,9) guarantee that the increase rate of the error subsystem p with unobservable pair (A p , C p ) is bounded. [8,10,17,35], the system considered in this section satisfies Assumption 1, which is universal in the application.…”

Section: Remarkmentioning

confidence: 99%

“…Conditions (8,9) guarantee that the increase rate of the error subsystem p with unobservable pair (A p , C p ) is bounded. [8,10,17,35], the system considered in this section satisfies Assumption 1, which is universal in the application. Also, the L 1 observer is proposed for the first time to guarantee the robustness with regard to exogenous disturbance w(t).…”

Section: Remarkmentioning

confidence: 99%

“…Thus, imposing a positive restriction on the designed observer for positive dynamical systems is often necessary. Recently, some problems of positive observer design for positive linear systems have been investigated in [8,10,17,27,29,32,35]. It is worth pointing out that the aforementioned literatures do not consider the effect of disturbances.…”

Section: Introductionmentioning

confidence: 99%

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Positive $$L_1 $$ L 1 Observer Design for Positive Switched Systems

Xiang

Karimi

2014

Circuits Syst Signal Process

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This paper investigates the problem of L 1 observer design for positive switched systems. Firstly, a new kind of positive L 1 observer is proposed for positive switched linear delay-free systems with observable and unobservable subsystems. Based on the average dwell time approach, a sufficient condition is proposed to ensure the existence of the positive L 1 observer. Under the condition obtained, the estimated error converges to zero exponentially, and the L 1 -gain from the disturbance input to the estimated error is less than a prescribed level. Then the proposed design result is extended to positive switched systems with mixed time-varying delays, where the mixed time-varying delays are presented in the form of discrete delay and distributed delay. Finally, two numerical examples are given to demonstrate the feasibility of the obtained results.

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Section: Remark 7 Compared With the Existing Results In The Literaturesmentioning

confidence: 99%

Section: Remark 7 Compared With the Existing Results In The Literaturesmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Positive $$L_1 $$ L 1 Observer Design for Positive Switched Systems

Xiang

Karimi

2014

Circuits Syst Signal Process

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Impulsive positive observers and dynamic output feedback stabilization of positive linear continuous systems

Xiao

Wang

et al. 2016

Intl J Robust & Nonlinear

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Summary This paper is concerned with the design and the synthesis of the impulsive positive observer (IPO) for positive linear continuous systems. The IPO can estimate the states for positive systems even when the measured output is only available at discrete‐time instants. In this paper, a time‐varying weighted copositive Lyapunov function is constructed, and the upper and lower bounds of impulsive intervals method combined with the convex combination technique are used to establish sufficient conditions for the existence of the IPO. Furthermore, the design of the dynamic output feedback controller based on the IPO is addressed to positively stabilize positive linear systems. Algorithms are given to design the IPO and the controller, respectively. Finally, two numerical examples are provided to show the effectiveness of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.

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Event‐triggered constrained control of positive systems with input saturation

Yin

Lin

Liu

et al. 2018

Intl J Robust & Nonlinear

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Summary This paper addresses the problem of event‐triggered stabilization for positive systems subject to input saturation, where the state variables are in the nonnegative orthant. An event‐triggered linear state feedback law is constructed. By expressing the saturated linear state feedback law on a convex hull of a group of auxiliary linear feedback laws, we establish conditions under which the closed‐loop system is asymptotically stable with a given set contained in the domain of attraction. On the basis of these conditions, the problem of designing the feedback gain and the event‐triggering strategy for attaining the largest domain of attraction is formulated and solved as an optimization problem with linear matrix inequality constraints. The problem of designing the feedback gain and the event‐triggering strategy for achieving fast transience response with a guaranteed size of the domain of attraction is also formulated and solved as an linear matrix inequality problem. The effectiveness of these results is then illustrated by numerical simulation.

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Observers for linear positive systems

Cited by 65 publications

References 23 publications

Positive $$L_1 $$ L 1 Observer Design for Positive Switched Systems

Positive $$L_1 $$ L 1 Observer Design for Positive Switched Systems

Impulsive positive observers and dynamic output feedback stabilization of positive linear continuous systems

Event‐triggered constrained control of positive systems with input saturation

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