Robust stability of time-delay systems

This paper analyzes the eigenvalue distribution of neutral differential systems and the corresponding difference systems, and establishes the relationship between the eigenvalue distribution and delay-independent stability of neutral differential systems. By using the "Complete Discrimination System for Polynomials", easily testable necessary and sufficient algebraic criteria for delay-independent stability of a class of neutral differential systems are established. The algebraic criteria generalize and unify the relevant results in the literature. Moreover, the maximal delay bound guaranteeing stability can be determined if the systems are not delay-independent stable. Some numerical examples are provided to illustrate the effectiveness of our results.

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“…Then condition (iii) in Theorem 1 is equivalent to the condition that (17) has no common real roots (z, y), z ∈ R, y ∈ R − {0}.…”

Section: Algebraic Criteria For Delay-independent Stability Of Neutramentioning

confidence: 99%

“…Similarly, by Lemma 6, the condition (iii) above is equivalent to one of the following conditions: (b1) when a 0 (y) = 0 or b 0 (y) = 0, R(f, g) has no nonzero real root, where R(f, g) is the resultant of (17).…”

Section: Algebraic Criteria For Delay-independent Stability Of Neutramentioning

confidence: 99%

Easily testable necessary and sufficient algebraic criteria for delay-independent stability of a class of neutral differential systems

Wei

Guan

Wang

2008

Systems & Control Letters

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“…Yang and Xu in [1] presented robust stability for an uncertain impulsive control system with time-varying delay. Li in [2] established robust exponential stability for impulsive systems with state-dependent delays, and several interesting results were established in [3][4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Robust exponential stability results for uncertain infinite delay differential systems with random impulsive moments

Vinodkumar

Senthilkumar

2018

Adv Differ Equ

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In this paper, we establish some criteria on robust exponential stability by using the formula for the variation of parameters and estimating the Cauchy matrix. More importantly, the robust stability criteria do not require the stability of the corresponding continuous system, and so they can be more widely applied to stabilize the unstable continuous system with time delays and uncertainties by using random impulsive control. Further, we give some numerical examples to illustrate the theoretical results.

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“…The first stability analysis is using the Dpartition method [38] and the root continuity property [39,40]. A growing body of literature has analyzed the stability of quasi polynomials (see [23,26,[41][42][43][44]). Particularly in [26], the delay phenomena have been studied for a fully actuated cart-pendulum system, introducing a full-state feedback controller with feedforward term, assuming that all velocities and positions are measurable.…”

Section: Introductionmentioning

confidence: 99%

Proportional Retarded Controller to Stabilize Underactuated Systems with Measurement Delays: Furuta Pendulum Case Study

Ortega-Montiel

Villafuerte-Segura

Vázquez³

et al. 2017

Mathematical Problems in Engineering

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The design and tuning of a simple feedback strategy with delay to stabilize a class of underactuated mechanical systems with dead time are presented. A linear time-invariant (LTI) model with time delay of fourth order and a Proportional Retarded (PR) controller are considered. The PR controller is shown as an appealing alternative to the application of observer-based controllers. This paper gives a step forward to obtain a better understanding of the effect of output delays and related phenomena in mechatronic systems, making it possible to design resilient control laws under the presence of uncertain time delays in measurements and obtain an acceptable performance without using a derivative action. The Furuta pendulum is a standard two-degrees-of-freedom benchmark example from the class of underactuated mechanical systems. The configuration under study includes an inherent output delay due to wireless communication used to transmit measurements of the pendulum's angular position. Our approach offers a constructive design and a procedure based on a combination of root loci and Mikhailov methods for the analysis of stability. Experiments over a laboratory platform are reported and a comparison with a standard linear state feedback control law shows the advantages of the proposed scheme.

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Robust stability of time-delay systems

Cited by 143 publications

References 12 publications

Easily testable necessary and sufficient algebraic criteria for delay-independent stability of a class of neutral differential systems

Easily testable necessary and sufficient algebraic criteria for delay-independent stability of a class of neutral differential systems

Robust exponential stability results for uncertain infinite delay differential systems with random impulsive moments

Proportional Retarded Controller to Stabilize Underactuated Systems with Measurement Delays: Furuta Pendulum Case Study

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