The symmetric linear matrix equation

Ran, André C. M.; Reurings, Martine

doi:10.13001/1081-3810.1075

Cited by 19 publications

(7 citation statements)

References 8 publications

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“…A significant extension of the results in [22] and [31] to the class of positive resolvent operators was provided by Damm and Hinrichsen in [7,8]. Similar results were derived also for discrete-time time-invariant case, see [16,30].…”

Section: Introductionsupporting

confidence: 57%

Exponential Stability for Discrete Time Linear Equations Defined by Positive Operators

Drăgan

Morozan

2005

Integr. equ. oper. theory

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In this paper the problem of exponential stability of the zero state equilibrium of a discrete-time time-varying linear equation described by a sequence of linear positive operators acting on an ordered finite dimensional Hilbert space is investigated.The class of linear equations considered in this paper contains as particular cases linear equations described by Lyapunov operators or symmetric Stein operators as well as nonsymmetric Stein operators. Such equations occur in connection with the problem of mean square exponential stability for a class of difference stochastic equations affected by independent random perturbations and Markovian jumping as well us in connection with some iterative procedures which allow us to compute global solutions of discrete time generalized symmetric or nonsymmetric Riccati equations.The exponential stability is characterized in terms of the existence of some globally defined and bounded solutions of some suitable backward affine equations (inequalities) or forward affine equations (inequalities). Mathematics Subject Classification (2000). Primary 39A11; Secondary 47H07, 93C55, 93E15.

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Section: Introductionsupporting

confidence: 57%

Exponential Stability for Discrete Time Linear Equations Defined by Positive Operators

Drăgan

Morozan

2005

Integr. equ. oper. theory

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“…Arguing now as in Ran and Reurings (2002), the matrix difference equation (A.19) can be written as the (n + 1) 2 × (n + 1) 2 linear system…”

Section: Discussionmentioning

confidence: 99%

Integral control for population management

et al. 2014

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We present a novel management methodology for restocking a declining population. The strategy uses integral control, a concept ubiquitous in control theory which has not been applied to population dynamics. Integral control is based on dynamic feedback-using measurements of the population to inform management strategies and is robust to model uncertainty, an important consideration for ecological models. We demonstrate from first principles why such an approach to population management is suitable via theory and examples.

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“…(see Ran and Reurings (2002)) and σ 2 = var (d(t)). The matrix C ∞ can be found as the limit of the iterative scheme…”

Section: Time-and Spatial-averaged Behaviourmentioning

confidence: 99%

Bounds on the dynamics of sink populations with noisy immigration

Eager

Guiver

Hodgson

et al. 2014

Theoretical Population Biology

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Sink populations are doomed to decline to extinction in the absence of immigration. The dynamics of sink populations are not easily modelled using the standard framework of per capita rates of immigration, because numbers of immigrants are determined by extrinsic sources (for example, source populations, or population managers). Here we appeal to a systems and control framework to place upper and lower bounds on both the transient and future dynamics of sink populations that are subject to noisy immigration. Immigration has a number of interpretations and can fit a wide variety of models found in the literature. We apply the results to case studies derived from published models for Chinook Salmon (Oncorhynchus tshawytscha) and blowout penstemon (Penstemon haydenii ).

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The symmetric linear matrix equation

Abstract: Abstract. In this paper sufficient conditions are derived for the existence of unique and positive definite solutions of the matrix equationsIn the case there is a unique solution which is positive definite an explicit expression for this solution is given.

Cited by 19 publications

References 8 publications

Exponential Stability for Discrete Time Linear Equations Defined by Positive Operators

Exponential Stability for Discrete Time Linear Equations Defined by Positive Operators

Integral control for population management

Bounds on the dynamics of sink populations with noisy immigration

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