Minimal eventually positive realizations of externally positive systems

Altafini, Claudio

doi:10.1016/j.automatica.2016.01.072

Cited by 28 publications

(19 citation statements)

References 22 publications

(32 reference statements)

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“…Finally, since eventually positive systems can be used to efficiently represent externally positive systems, some of the results for internally positive systems are expected to remain true for these systems as well; see e.g. [58,59].…”

Section: General Theoretical Resultsmentioning

confidence: 99%

Stability and performance analysis of linear positive systems with delays using input–output methods

Briat

2017

International Journal of Control

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It is known that input-output approaches based on scaled small-gain theorems with constant Dscalings and integral linear constraints are non-conservative for the analysis of some classes of linear positive systems interconnected with uncertain linear operators. This dramatically contrasts with the case of general linear systems with delays where input-output approaches provide, in general, sufficient conditions only. Using these results we provide simple alternative proofs for many of the existing results on the stability of linear positive systems with discrete/distributed/neutral time-invariant/-varying delays and linear difference equations. In particular, we give a simple proof for the characterization of diagonal Riccati stability for systems with discrete-delays and generalize this equation to other types of delay systems. The fact that all those results can be reproved in a very simple way demonstrates the importance and the efficiency of the input-output framework for the analysis of linear positive systems. The approach is also used to derive performance results evaluated in terms of the L1-, L2-and L∞-gains. It is also flexible enough to be used for design purposes.

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Section: General Theoretical Resultsmentioning

confidence: 99%

Stability and performance analysis of linear positive systems with delays using input–output methods

Briat

2017

International Journal of Control

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“…Under proper assumptions, any PIR transfer function admits a positive realisation [11], which is nonminimal: to find a state space representation that is inputoutput monotone, the state needs to be artificially augmented. This augmentation can be avoided, under some assumptions, by considering eventually positive minimal realisations [2].…”

Section: Properties Of Pir Transfer Functions and Decompositionmentioning

confidence: 99%

Aggregates of positive impulse response systems: A decomposition approach for complex networks

Bianchini

Samaniego

Franco

et al. 2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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Abstract-To simplify the analysis of complex dynamical networks, we have recently proposed an approach that decomposes the overall system into the sign-definite interconnection of subsystems with a Positive Impulse Response (PIR). PIR systems include and significantly generalise input-output monotone systems, and the PIR property (or equivalently, for linear systems, the Monotonic Step Response property) can be evinced from experimental data, without an explicit model of the system. An aggregate of PIR subsystems can be associated with a signed matrix of interaction weights, hence with a signed graph where the nodes represent the subsystems and the arcs represent the interactions among them. In this paper, we prove that stability is structurally ensured (for any choice of the PIR subsystems) if a Metzler matrix depending on the interaction weights is Hurwitz; this condition is non-conservative. We also show how to compute an influence matrix that represents the steady-state effects of the interactions among PIR subsystems.

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“…presented the exact computation of ℓ 1 ‐induced norm in , which is proved to be more useful for the positive systems than other performance indices such as

H_{\infty}

norm and ℓ 2 ‐induced norm. Moreover, many interesting results have been published thereafter (see and references therein).…”

Section: Introductionmentioning

confidence: 99%

Weighted‐average ℓ₁ filtering for switched positive systems

Ren

Sun

Feng

et al. 2017

Intl J Robust & Nonlinear

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Summary In this paper, the filtering problem for a class of switched positive systems with dwell time is investigated. A novel weighted‐average technique is proposed for filter design such that the final estimate of the unmeasurable outputs of the considered system is more accurate than that of traditional approaches. The main contributions of this paper are summarized as follows: By exploiting the positivity and characteristics of switched positive systems with dwell time, a candidate linear copositive Lyapunov function, which is both quasi‐time‐dependent and mode‐dependent, is presented to establish the closed‐loop stability of the considered systems. Upon the established closed‐loop stability, less conservative bounded positive filters (both upper‐bound and lower‐bound filter) with ℓ1 disturbance attenuation performance are designed for the considered system. By introducing a proper weight, a weighted‐average approach, which is more general than the bounded filter design method, is proposed for filter design. The worst ℓ1 disturbance attenuation performance of the novel developed filter is evaluated. Both the bounded filters and the weighted‐average filter are designed by solving standard linear programming problems. A numerical example illustrates the effectiveness of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd.

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Minimal eventually positive realizations of externally positive systems

Cited by 28 publications

References 22 publications

Stability and performance analysis of linear positive systems with delays using input–output methods

Stability and performance analysis of linear positive systems with delays using input–output methods

Aggregates of positive impulse response systems: A decomposition approach for complex networks

Weighted‐average ℓ₁ filtering for switched positive systems

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Minimal eventually positive realizations of externally positive systems

Cited by 28 publications

References 22 publications

Stability and performance analysis of linear positive systems with delays using input–output methods

Stability and performance analysis of linear positive systems with delays using input–output methods

Aggregates of positive impulse response systems: A decomposition approach for complex networks

Weighted‐average ℓ1 filtering for switched positive systems

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Product

Resources

About

Weighted‐average ℓ₁ filtering for switched positive systems