On Linear Copositive Lyapunov Functions and the Stability of Switched Positive Linear Systems

Mason, Oliver; Shorten, Robert

doi:10.1109/tac.2007.900857

Cited by 371 publications

(210 citation statements)

References 9 publications

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“…Inspired by this and related work, and by our interest in switched systems, we intend in this brief paper to determine tractable conditions for the existence of a common LCLF for a finite number of LTI systems that are associated with polyhedral regions in the positive orthant, which can be interpreted as state dependent switching. As we shall see, compact and easily verifiable conditions can be obtained for the existence of such a function, and these results complement and complete initial results reported in [17].…”

Section: Introductionsupporting

confidence: 83%

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On linear co-positive Lyapunov functions for sets of linear positive systems

2009

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In this paper we derive necessary and sufficient conditions for the existence of a common linear co-positive Lyapunov function for a finite set of linear positive systems. Both the state dependent and arbitrary switching cases are considered. Our results reveal an interesting characterisation of "linear" stability for the arbitrary switching case; namely, the existence of such a linear Lyapunov function can be related to the requirement that a number of extreme systems are Metzler and Hurwitz stable. Examples are given to illustrate the implications of our results.

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Section: Introductionsupporting

confidence: 83%

“…Remark We shall see in the next section that Theorem 2 leads directly to very elegant conditions for the existence of a common LCLF, and give very interesting insights into the stability of positive switched linear systems, completing initial work reported in [17].…”

Section: State Dependent Switching Of Positive Systemsmentioning

confidence: 53%

On linear co-positive Lyapunov functions for sets of linear positive systems

2009

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“…Recently, there has been an increasing research interest in the control problems of switched positive systems in virtue of their significance in both theory and applications [4]- [10]. Several methods have been proposed to deal with the switching characteristics and positivity preservation, which include the average dwell time technique [5], the multiple Lyapunov function approach [4] as well as the switched Lyapunov function approach [6], etc.…”

Section: Introductionmentioning

confidence: 99%

“…Several methods have been proposed to deal with the switching characteristics and positivity preservation, which include the average dwell time technique [5], the multiple Lyapunov function approach [4] as well as the switched Lyapunov function approach [6], etc. It is worth noticing that, in almost all relevant literature, the subsystems have been assumed to be linear.…”

Section: Introductionmentioning

confidence: 99%

Distributed Filtering for Switched Nonlinear Positive Systems With Missing Measurements Over Sensor Networks

Wang

et al. 2016

IEEE Sensors J.

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Abstract-In this paper, the distributed filtering problem is investigated for a class of switched nonlinear positive systems over sensor networks. The randomly varying nonlinearities and missing measurements, which are governed by two mutually independent Bernoulli distributed white sequences, are taken into account. Based on the output measurements of the individual sensor and its neighbors, the distributed filter with positivity constraint is designed to ensure the prescribed average l∞ performance index of the estimation error dynamics. Special attention is paid to preserve the positivity of the underlying system as well as the sparseness of the addressed network topology. Sufficient conditions are established on the existence of the desired filters by using the linear programming approach and the filter gains are subsequently characterized. A simulation example is provided to illustrate the effectiveness of the proposed filtering method.

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“…Proof It follows from Lemma 2 and (38) that systems (25) and (26) are positive. Construct the following piecewise co-positive type Lyapunov-Krasovskii functional for system (26) …”

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confidence: 95%

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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On Linear Copositive Lyapunov Functions and the Stability of Switched Positive Linear Systems

Cited by 371 publications

References 9 publications

On linear co-positive Lyapunov functions for sets of linear positive systems

On linear co-positive Lyapunov functions for sets of linear positive systems

Distributed Filtering for Switched Nonlinear Positive Systems With Missing Measurements Over Sensor Networks

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

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