Delay-dependent H&lt;inf&gt;&amp;#x221E;&lt;/inf&gt; control of linear systems with time-varying delays using proportional-derivative state feedback

Shariati, A.; Taghirad, Hamid D.; Labibi, B.

doi:10.1109/med.2010.5547738

Cited by 6 publications

(6 citation statements)

References 13 publications

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“…being 0 null matrices of suitable dimensions. Given the attenuation index J as in (17), following [53,55] the robust formation containment is guaranteed iḟ…”

Section: Theoremmentioning

confidence: 99%

A L2‐gain robust PID‐like protocol for time‐varying output formation‐containment of multi‐agent systems with external disturbance and communication delays

Tommasi

Lui

Petrillo

et al. 2021

IET Control Theory & Appl

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This paper addresses the time-varying output formation-containment control problem for homogeneous high-order linear Multi-Agent Systems (MASs). In this context, a PID-like output-feedback control strategy is proposed capable to guarantee that all followers reach and maintain a time-varying formation reference behaviour, as imposed by the multiple leaders, while keeping a prescribed offset with respect to it. Moreover, the proposed approach allows dealing with both communication impairments and external disturbances acting on agents dynamics. The asymptotic stability of the closed-loop MAS is analytically proved by means of a Lyapunov-Krasovskii approach. Stability conditions are expressed as a feasibility problem with Linear Matrix Inequalities constraints, whose solution provides the proper tuning of the robust PID control gains. Extensive numerical analysis confirms the theoretical framework and discloses the effectiveness of the proposed approach in ensuring the output time-varying formation-containment. 1 This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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“…being 0 null matrices of suitable dimensions. Given the attenuation index J as in (17), following [53,55] the robust formation containment is guaranteed iḟ…”

Section: Theoremmentioning

confidence: 99%

A L2‐gain robust PID‐like protocol for time‐varying output formation‐containment of multi‐agent systems with external disturbance and communication delays

Tommasi

Lui

Petrillo

et al. 2021

IET Control Theory & Appl

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“…Moreover, delay-dependent H ∞ filtering conditions were proposed for uncertain neutral stochastic systems with Markovian switching and mode-dependent time delays [22]. By applying a H ∞ state-feedback controller in [23], a neutral-type time-delay system was studied. And in another paper [24], the H ∞ feedback controller was used to obtain the results.…”

Section: Introductionmentioning

confidence: 99%

Improved Results on Delay-Dependent Robust $H_{\infty}$ Control of Uncertain Neutral Systems with Mixed Time-Varying Delays

Zhang

et al. 2021

Mathematical Problems in Engineering

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In this paper, the problem of the delay-dependent robust H ∞ control for a class of uncertain neutral systems with mixed time-varying delays is studied. Firstly, a robust delay-dependent asymptotic stability criterion is shown by linear matrix inequalities (LMIs) after introducing a new Lyapunov–Krasovskii functional (LKF). The LKF including vital terms is expected to obtain results of less conservatism by employing the technique of various efficient convex optimization algorithms and free matrices. Then, based on the obtained criterion, analyses for uncertain systems and H ∞ controller design are presented. Moreover, on the analysis of the state-feedback controller, different from the traditional method which multiplies the matrix inequality left and right by some matrix and its transpose, respectively, we can obtain the state-feedback gain directly by calculating the LMIs through the toolbox of MATLAB in this paper. Finally, the feasibility and validity of the method are illustrated by examples.

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“…However, most results were developed for systems with constant delays, and only a few works have paid special attention to the use of the PID controller for the processes with uncertain delays. In recent years, since the development of networked control system, some research has focused on the design of PID controllers for the systems with time-varying delays [3]- [5], [18]- [20]. In [19] and [20], the authors used the stability criterion proposed by Kao [21] to design a PID controller; in [3]- [5], the stability was considered by solving a sets of LMIs.…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, since the development of networked control system, some research has focused on the design of PID controllers for the systems with time-varying delays [3]- [5], [18]- [20]. In [19] and [20], the authors used the stability criterion proposed by Kao [21] to design a PID controller; in [3]- [5], the stability was considered by solving a sets of LMIs. Although time-varying delay can be considered as the special case of uncertain delay, the stability criterion for time-varying delay is conservative if it is directly used to study the stability of the systems with general uncertain delays.…”

Section: Introductionmentioning

confidence: 99%

Control Design for Disturbance Rejection in the Presence of Uncertain Delays

Jin

Liu

Huang

2017

IEEE Trans. Automat. Sci. Eng.

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This paper is concerned with control of processes with uncertain delays for disturbance rejection. The effect of the uncertain delays on the stability is studied. First, the method to compute the maximum uncertain delay that a given controller can tolerate is described. Second, in the case of PI/PID controller, all of the admissible controller parameters stabilizing a system with uncertain but bounded delays are determined. Meanwhile, we propose a simple method to construct the parameter space satisfying a given robustness index for the nominal model. In the admissible regions satisfying various objectives, the global optimum controller is achieved for disturbance rejection in the presence of uncertain delay. As a result, the MIGO ( -constrained Integral Gain Optimization) method is revisited in the case of uncertain delay, and the rule of selecting the value of maximum sensitivity function is proposed in terms of the bound on the uncertain delay. Two simulation examples and an experiment are given to demonstrate the effectiveness and advantage of the proposed method.Note to Practitioners-The practitioners can use the methods presented in this paper to solve the following two problems: 1) to estimate the allowable delay that a control system can tolerate and 2) to design the globally optimal PID controller in terms of the delay range. This paper was motivated by how to find the globally optimal PID parameters in the presence of uncertain delays. Conventionally, the uncertain delay is dealt with linear matrix inequalities (LMIs). However, the results based on solving LMIs are not globally optimal. Here, we dealt with the uncertain delay in the frequency domain. We not only proposed a method to compute the maximum delay that the classical PID controller can tolerate but also find all the admissible PID controllers stabilizing a processes in the presence of uncertain delay. To obtain the globally optimal controller for a given process, the boundaries for the norm-based indices were constructed. Then, the globally optimal PID controller satisfying multiple objectives can be easily found in the admissible region. The examples clearly showed that the method based on LMI only provided one local optimal solution. However, the proposed method can find all of the admissible solutions and select the optimal one. We also discussed the application of the well-known MIGO method in the case of uncertain delays. Also, the rules of selecting the robustness index in terms of uncertain delay were proposed. The above methods were proposed based on first-order plus time delay models since Manuscript most chemical processes can be modeled by this type of model. Certainly the methods can be extended to high order processes with uncertain delays. But the methods may not easily be used for multiple-input-multiple-output processes since it is difficult to construct the stability regions of the parameters for such processes. Also, the method cannot be used to deal with the random delays.Index Terms-Parameter space, PID controller, sensitiv...

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Delay-dependent H<inf>∞</inf> control of linear systems with time-varying delays using proportional-derivative state feedback

Cited by 6 publications

References 13 publications

A L2‐gain robust PID‐like protocol for time‐varying output formation‐containment of multi‐agent systems with external disturbance and communication delays

A L2‐gain robust PID‐like protocol for time‐varying output formation‐containment of multi‐agent systems with external disturbance and communication delays

Improved Results on Delay-Dependent Robust $H_{\infty}$ Control of Uncertain Neutral Systems with Mixed Time-Varying Delays

Control Design for Disturbance Rejection in the Presence of Uncertain Delays

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Delay-dependent H<inf>&#x221E;</inf> control of linear systems with time-varying delays using proportional-derivative state feedback

Cited by 6 publications

References 13 publications

A L2‐gain robust PID‐like protocol for time‐varying output formation‐containment of multi‐agent systems with external disturbance and communication delays

A L2‐gain robust PID‐like protocol for time‐varying output formation‐containment of multi‐agent systems with external disturbance and communication delays

Improved Results on Delay-Dependent Robust H ∞ Control of Uncertain Neutral Systems with Mixed Time-Varying Delays

Control Design for Disturbance Rejection in the Presence of Uncertain Delays

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Delay-dependent H<inf>∞</inf> control of linear systems with time-varying delays using proportional-derivative state feedback

Improved Results on Delay-Dependent Robust $H_{\infty}$ Control of Uncertain Neutral Systems with Mixed Time-Varying Delays