On monotonicity of solutions of nonnegative and compartmental dynamical systems with time delays

This paper is concerned with exponential stability analysis for linear continuous positive systems with bounded time-varying delay. Our approach is based on Lyapunov-Krasovskii functional with delay decomposition. The main idea is to divide uniformly the discrete delay interval into multiple segments and then to choose proper functionals with different weighted matrices corresponding to different segments. The synthesis of our delay-dependent sufficient stability criteria is formulated in terms of linear matrix inequalities. The proposed results are shown to be less conservative compared to other results from the literature. Some illustrative examples are given to show the effectiveness of the obtained results.

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“…According to this definition, we need to find under which condition the delayed system (1) is positive (see for example [3,10]). …”

Section: Definitionmentioning

confidence: 99%

Exponential Stability Criteria for Positive Systems with Time-Varying Delay: A Delay Decomposition Technique

Elloumi¹,

Mehdi²,

Chaabane³

et al. 2015

Circuits Syst Signal Process

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show abstract

“…According to this definition, we need to find the condition under which the delayed system (1) is positive (see for example [19,24]). …”

Section: Preliminariesmentioning

confidence: 99%

Delay-dependent Stabilization Conditions of Controlled Positive Continuous-time Systems

Elloumi

Benzaouia

Chaabane

2014

Int. J. Autom. Comput.

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The stabilization problem for a class of linear continuous-time systems with time-varying non differentiable delay is solved while imposing positivity in closed-loop. In particular, the synthesis of state-feedback controllers is studied by giving sufficient conditions in terms of linear matrix inequalities (LMIs). The obtained results are then extended to systems with non positive delay matrix by applying a memory controller. The effectiveness of the proposed method is shown by using numerical examples.

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“…+ for all t ≥ 0. According to this definition, we need to find under which condition the delayed system (1) is positive (see for example [6], [14]). Lemma 2.1.…”

Section: Delayed Positive Systemsmentioning

confidence: 99%

“…17th IFAC World Congress (IFAC'08) Seoul, Korea, July [6][7][8][9][10][11]2008 The left side of this equation is nonpositive (because λ > 0 and x(t) ≥ 0) and the right side is nonnegative (because λ > 0, x(t) ≥ 0 and A 1 ≥ 0). Thus, the only possibility is that x(t) = 0.…”

Section: Delayed Positive Systemsmentioning

confidence: 99%

“…17th IFAC World Congress (IFAC'08) Seoul, Korea, July [6][7][8][9][10][11]2008 Then, computing BKd = B n i=1 y i and using condition (17) leads to (A + A 1 + BK)d < 0. Since A + BK is a Metzler matrix, A 1 is nonnegative and d > 0, using Theorem 2.1, we can conclude that the delayed closedloop system (2) is positive asymptotically stable for any r > 0.…”

Section: Controller Synthesismentioning

confidence: 99%

See 1 more Smart Citation

Memoryless Control to Drive States of Delayed Continuous-time Systems within the Nonnegative Orthant

Hmamed

Benzaouia

Rami

et al. 2008

IFAC Proceedings Volumes

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On monotonicity of solutions of nonnegative and compartmental dynamical systems with time delays

Cited by 4 publications

References 17 publications

Exponential Stability Criteria for Positive Systems with Time-Varying Delay: A Delay Decomposition Technique

Exponential Stability Criteria for Positive Systems with Time-Varying Delay: A Delay Decomposition Technique

Delay-dependent Stabilization Conditions of Controlled Positive Continuous-time Systems

Memoryless Control to Drive States of Delayed Continuous-time Systems within the Nonnegative Orthant

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