Stability boundaries of mechanical controlled system with time delay

Ramachandran, P.; Ram, Yitshak M.

doi:10.1016/j.ymssp.2011.09.017

Cited by 29 publications

(13 citation statements)

References 10 publications

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“…4 It can be seen that with this controller, the feedback system is positive and the state evolution of the system remains always within the nonnegative orthant. For example, the state trajectories from several initial positive conditions can be seen in Fig.…”

Section: Examplesmentioning

confidence: 99%

“…The main objective is to build state-feedback controllers that make the closed-loop system with time-varying delay α-exponentially stable and positive. This class of systems is frequently encountered in many fields of science and engineering, especially in biological modeling, economics, physiology and many others (see [1][2][3][4]). Since the existence of delay is generally a source of instability and degradation of performance, many researches and contributions have been done to analyze stability of linear systems with time-varying delay (see [5][6][7][8]).…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Elloumi

Benzaouia

Chaabane

2014

Int. J. Autom. Comput.

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“…Time delays can inherently appear in many engineering systems with feedback control including, magnetic bearing systems [1], manufacturing process [2][3][4][5][6], microelectromechanical systems [7], actively controlled mechanical systems [8], vehicle systems [9,10], and spacecraft [11]. Such systems have been referred to as timedelayed nonlinear systems in order to distinguish them from conventional nonlinear systems without time delay, and concurrently time-delayed nonlinear equations used to represent the corresponding mathematical models [12].…”

Section: Introductionmentioning

confidence: 99%

Coexistence of two families of sub-harmonic resonances in a time-delayed nonlinear system at different forcing frequencies

Zhou

2017

Mechanical Systems and Signal Processing

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Two coexisting families of sub-harmonic resonances can be induced at different forcing frequencies in a time-delayed nonlinear system having quadratic nonlinearities. They occur in the region where two stable bifurcating periodic solutions coexist in the corresponding autonomous system following two-to-one resonant Hopf bifurcations of the trivial equilibrium. The forced response is found to demonstrate small-and largeamplitude quasi-periodic motion under the family of sub-harmonic resonances related to Hopf bifurcation frequencies, and large-amplitude periodic and quasi-periodic motion under the family of sub-harmonic resonances associated with the shifted Hopf bifurcation frequencies. The family of sub-harmonic resonances related to Hopf bifurcation frequencies may cease to exist with the loss of the initially established frequency relationship of sub-harmonic resonances when the magnitude of periodic excitation is beyond a certain value. This will lead to a jump phenomenon from small-to largeamplitude quasi-periodic motion. Bifurcation diagrams, time trajectories and frequency spectra are numerically obtained to characterize the sub-harmonic resonances of the time-delayed nonlinear system around the critical point of the resonant Hopf bifurcations.

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“…Time delays are usually encountered in various fields of science and engineering, especially in biological modeling, economics, thermal systems and many others (see [2,11,15,19,22]). While general linear systems tend to be sensitive to time delays and consequently become oscillatory or even unstable, it has been shown that for linear positive systems with constant delays or bounded time-varying delays, the asymptotic stability is not related to the magnitudes of delays but only depends on the system matrices [7,9,13,14,20].…”

Section: Introductionmentioning

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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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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Stability boundaries of mechanical controlled system with time delay

Cited by 29 publications

References 10 publications

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

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

Coexistence of two families of sub-harmonic resonances in a time-delayed nonlinear system at different forcing frequencies

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

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