Characterization of Delay‐Independent Stability and Delay Interference Phenomena

Michiels, Wim; Niculescu, Silviu–Iulian

doi:10.1137/050641223

Cited by 39 publications

(15 citation statements)

References 16 publications

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“…Many control problems have been extensively studied with many results reported in the literature. These problems include, among others, filtering [35], stability analysis and stabilization [25,39], H ∞ control and prediction [38,40], robust control [37], and passive control [9]. Among the problems studied in the literature, stability is one of the most fundamental (see, for example, [3,4,8,11,15,19,26,36] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Global and Semi-Global Stabilization of Linear Systems With Multiple Delays and Saturations in the Input

Zhou¹,

Lin²,

Duan³

2010

SIAM J. Control Optim.

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This paper studies stabilization problems for linear systems with multiple delays in the input. Two types of delays are considered. The first type of delays is constant delays, which can be arbitrarily large, while the second type is time-varying with an arbitrarily large bound. With the first type of delays, under the condition that the open loop system is absolutely controllable with all its eigenvalues on the imaginary axis, (globally) stabilizing state and output feedback laws are constructed based on the solution to a family of parametric Riccati equations, which can be obtained explicitly through the solution of a parametric linear matrix equation. With the second type of delays, under the condition that the open-loop system is absolutely controllable with all its eigenvalues on the imaginary axis being zero, (global) state and output feedback laws are explicitly constructed based on the solution to a similar family of parametric Riccati equations. When the input is also subject to magnitude saturation, it is shown that semiglobal stabilization, instead of global stabilization, can still be achieved. Numerical examples illustrate the effectiveness of the proposed approach.

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Section: Introductionmentioning

confidence: 99%

Global and Semi-Global Stabilization of Linear Systems With Multiple Delays and Saturations in the Input

Zhou¹,

Lin²,

Duan³

2010

SIAM J. Control Optim.

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“…It is a permanent magnet direct current (PMDC) motor and all the necessary information and all operating conditions about the motor can be found in [21]. However, since the motor parameters are not explicitly known, a system identification process is taken into account from the real data obtained from the motors.…”

Section: Identification Of the Systemmentioning

confidence: 99%

“…Using the methodology given in [17], a servomechanism subject to teleoperation is considered in this paper. The motors are selected as Dynamixel MX-106T [21] and as the motor parameters are not explicitly given, the global optimization method, named Genetic Algorithm (GA) is employed to obtain a proper model of the motors. Then using the obtained mathematical model, all gains providing time-delay independent stability is computed as proposed in [17], and it is shown that the simulation results are as expected.…”

Section: Introductionmentioning

confidence: 99%

Robust Stabilization of a Servomechanism With Respect To Time-Delay

Nesimioğlu

Yılmaz

Dincel³

2016

International Journal of Applied Mathematics, Electronics and Computers

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Abstract:In this paper, a servomechanism under teleoperation is considered. Since the teleoperation itself can result in large amount of time-delays and this amount can change operation to operation, it can be difficult to control such mechanisms in order to accomplish the desired tasks. From the robust control viewpoint, a methodology that guarantees the stability in worst case is essential. Based on a simple methodology to find the delay independent stabilizing proportional (P) controller regions, just by forming the magnitude polynomial and employing the root locus technique, the stability of the robot is guaranteed, even in the worst case: the system becomes stable even if the connection has huge amount of time-delays. This fact is evidenced first by the simulations. To simulate the real system, as there is no information about the motor parameters, the motor is modeled by a global optimization methodology, named Genetic Algorithm in order to obtain a valid model for the system as accurate as possible. Then the resulting P controllers are applied to the real system, the results of which are found in accordance with the simulation results; the stability of the operation is not affected by the time-delay.

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“…Namely, positions of vertical strips of poles are sensitive to infinitesimal delay changes, which give rise to the notion of strong stability [10,11] that is affected i.a. by the rational dependence of delays [9].…”

Section: Introductionmentioning

confidence: 99%

“…Much effort has been made to analyse the infinite spectrum of TDS of retarded as well as neutral type (NTDS), mainly when the endeavour to decide about system stability and its dependence on particular delays' values [3][4][5][6][7][8]. Compared to retarded ones, NTDS are much more advanced, tricky and intricate regarding spectral properties [1,4,9]. Namely, positions of vertical strips of poles are sensitive to infinitesimal delay changes, which give rise to the notion of strong stability [10,11] that is affected i.a.…”

Section: Introductionmentioning

confidence: 99%

A comparison of possible exponential polynomial approximations to get commensurate delays

Pekař

Chalupa

2016

MATEC Web Conf.

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Abstract. The paper is aimed at a comparative simulation study on three prospective ideas how to approximate a general exponential polynomial by another one having all its exponents in the exp-function as integer multiples of some real number. This work is motivated by spectral properties of neutral time-delay systems (NTDS) and the contemporary state of the knowledge about the spectrum of NTDS with commensurate delays which are characterized by the latter family of exponential polynomials. The three ideas are, namely, those: Taylor series expansion, the interpolation in points given by dominant roots estimates and the special extrapolation technique presented by the authors recently. The goal is to match dominant parts of both the spectra as close as possible. However, some properties from the so called strong stability point of view can not be, in principle, preserved. The presented simulation example demonstrates the accuracy and efficiency of all the methods.

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Characterization of Delay‐Independent Stability and Delay Interference Phenomena

Cited by 39 publications

References 16 publications

Global and Semi-Global Stabilization of Linear Systems With Multiple Delays and Saturations in the Input

Global and Semi-Global Stabilization of Linear Systems With Multiple Delays and Saturations in the Input

Robust Stabilization of a Servomechanism With Respect To Time-Delay

A comparison of possible exponential polynomial approximations to get commensurate delays

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