Dissipativity Theory for Nonnegative and Compartmental Dynamical Systems With Time Delay

Haddad, Wassim M.; Chellaboina, VijaySekhar; Rajpurohit, Tanmay

doi:10.1109/tac.2004.825967

Cited by 55 publications

(13 citation statements)

References 12 publications

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“…The result is derived via the construction of a novel linear Lyapunov functionals for multi-stage case. For the Lyapunov-based analysis of positive linear time-delay systems, as well as nonlinear systems with the nonlinearities subject to a sector bound, we refer to [6], [10], [11], [14]. In a simpler model of hematopoiesis (without fast self-renewal) our conditions guarantee global exponential stability with a given decay rate.…”

Section: Introductionmentioning

confidence: 99%

Stability of the cell dynamics in acute myeloid leukemia

Fridman

Bonnet

Mazenc

et al. 2016

Systems & Control Letters

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International audienceIn this paper we analyze the global asymptotic stability of the trivial solution for a multi-stage maturity acute myeloid leukemia model. By employing the positivity of the corresponding nonlinear time-delay model, where the nonlin-earity is locally Lipschitz, we establish the global exponential stability under the same conditions that are necessary for the local exponential stability. The result is derived for the multi-stage case via a novel construction of linear Lyapunov functionals. In a simpler model of hematopoiesis (without fast self-renewal) our conditions guarantee also global exponential stability with a given decay rate. Moreover, in this simpler case the analysis of the PDE model is presented via novel Lyapunov functionals for the transport equations

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Section: Introductionmentioning

confidence: 99%

Stability of the cell dynamics in acute myeloid leukemia

Fridman

Bonnet

Mazenc

et al. 2016

Systems & Control Letters

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“…Naturally, the linear Lyapunov function can be applied as a valid candidate for stability analysis and controller synthesis of positive systems. By using the linear Lyapunov approach, stability analysis, L 1 -gain performance analysis and control design have been discussed for positive continuous-time linear systems [3], [13], [24] and positive continuous-time switched systems with delays [14], [19], [20]. In this paper, two types of admissible input signals are considered based on 1-norm and/or ∞-norm.…”

Section: Introductionmentioning

confidence: 99%

On reachable sets for positive linear systems under constrained exogenous inputs

Lam

Shu

et al. 2016

Automatica

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This paper focuses on positive linear time-invariant systems with constant coefficients and specific exogenous disturbance. The problem of finding a hyper-pyramid to bound the set of the states that are reachable from the origin in the Euclidean space is addressed, subject to inputs whose (1, 1)-norm or (∞, 1)-norm is bounded by a prescribed constant. The Lyapunov approach is applied and a bounding hyper-pyramid is obtained by solving a set of inequalities. Iterative procedures (with an adjustable parameter) for reducing the hyper-volume of the bounding hyper-pyramid for the reachable set are proposed.

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“…in the work of Haddad et al, 32 where q and r are vectors of appropriate dimensions. The following definitions are regarded as an extension of general switched systems to PSLSs case.…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

Dissipativity and dissipative control for positive switched systems: A multiple linear copositive storage function method

Wang

Zhao

2019

Intl J Robust & Nonlinear

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Summary In this article, the problems of dissipativity analysis and dissipative control are investigated for positive switched linear systems in both continuous and discrete‐time domains. We aim at solving the problems via employing a multiple linear copositive storage function scheme. The solvability of the problems for individual subsystem is only on their active regions. Switching laws and a set of feedback controllers are jointly devised such that the associated closed‐loop switched systems are not only positive but also dissipative, which is from the exogenous input to the output. Asymptotic stability is derived if all subsystems are zero‐state detectable. Moreover, sufficient conditions guaranteeing dissipativity with positivity constraint are presented, which can be easily examined on the grounds of linear programming approach. Finally, an example is offered, illustrating that the proposed control strategy is successful.

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Dissipativity Theory for Nonnegative and Compartmental Dynamical Systems With Time Delay

Cited by 55 publications

References 12 publications

Stability of the cell dynamics in acute myeloid leukemia

Stability of the cell dynamics in acute myeloid leukemia

On reachable sets for positive linear systems under constrained exogenous inputs

Dissipativity and dissipative control for positive switched systems: A multiple linear copositive storage function method

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