Anti-windup design with guaranteed regions of stability for discrete-time linear systems

Silva, J.M.G. da; Tarbouriech, Sophie

doi:10.23919/acc.2004.1384694

Cited by 17 publications

(15 citation statements)

References 15 publications

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“…In this control design, our goal is to design the controller (5) in the presence of saturation. Differently to the first case, we will permit the saturation limits.…”

Section: Saturated Controlmentioning

confidence: 99%

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H∞ control of multiple model subject to actuator saturation: application to quarter-car suspension system

Saifia

Chadli

Labiod

2011

Analog Integr Circ Sig Process

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This paper deals with the H ? control of nonlinear systems in multiple model representation subject to actuator saturation. An application to Quarter-Car suspension system under actuator saturation is then given using the multiple model approach. The concept of so-called parallel distributed compensation (PDC) is employed for designing control system. The idea of this controller consists in designing a linear feedback control for each local linear model. To address the input saturation problem in this paper, both constrained and saturated controls input cases are proposed. In the two cases, H ? stabilization conditions in the sense of Lyapunov method are derived. Moreover, a controller design with larger attraction domain is formulated and solved as a linear matrix inequality (LMI) optimization problem. Our simulation results show that both the saturated and constrained controls can stabilize the resulting closed-loop suspension system and eliminate the effect of external disturbances. Indeed, the main roles of car suspension systems, which consist on improving ride comfort of passengers and the road holding capacity of the vehicle, are achieved.

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“…In this control design, our goal is to design the controller (5) in the presence of saturation. Differently to the first case, we will permit the saturation limits.…”

Section: Saturated Controlmentioning

confidence: 99%

“…This problem has been receiving increasing attention for control of both linear [2][3][4][5][6] and nonlinear systems [7,10,19]. Generally, the stabilization of system in the presence of saturation can be dealt by tow methods.…”

Section: Introductionmentioning

confidence: 99%

H∞ control of multiple model subject to actuator saturation: application to quarter-car suspension system

Saifia

Chadli

Labiod

2011

Analog Integr Circ Sig Process

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“…One of the most relevant approaches to the analysis of saturated systems is based on a linear difference inclusion (LDI) of the saturation non-linearity (see [1,11], and the references therein). Recently, in [9,10] a modified sector condition, which is new and original, has been developed to study the determination of stability regions. Compared with previous works (for example [11] in which saturation is modeled by the polytopic LDIs), one advantage of the conditions obtained by the application of the proposed modified sector condition in [4,10] is that the results are less complex than previous ones.…”

mentioning

confidence: 99%

“…Recently, in [9,10] a modified sector condition, which is new and original, has been developed to study the determination of stability regions. Compared with previous works (for example [11] in which saturation is modeled by the polytopic LDIs), one advantage of the conditions obtained by the application of the proposed modified sector condition in [4,10] is that the results are less complex than previous ones. This advantage enable us to have the potential to design more sophisticated parameter-dependent Lyapunov function to investigate the saturated system.…”

mentioning

confidence: 99%

“…Considering the time-varying parameters, we proposed a homogeneous polynomially parameter-dependent matrix function (HPP-DMF for abbreviation). Then, a set invariance condition is obtained by applying the HPP-DMF to the Lyapunov function and control law along with the using of the modified sector condition in [9,10]. Sequently, an algorithm is proposed to minimize the worst-case performance.…”

mentioning

confidence: 99%

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Gain Scheduled State Feedback Control for Discrete-Time-Varying Polytopic Systems Subject to Input Saturation

Wang

Liu

2011

Circuits Syst Signal Process

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In this paper, we study the stability and performance optimization problem of discrete-time-varying polytopic systems with actuator saturation. First, the homogeneous polynomially parameter-dependent matrix function (HPP-DMF for abbreviation) is proposed. Then, a set invariance condition is obtained by applying the HPP-DMF to the Lyapunov function and gain scheduled control law. Based on the set invariance condition, an algorithm is proposed to minimize the worst-case performance. The conditions in the algorithm are expressed in terms of linear matrix inequalities (LMIs). In addition, it is shown that as the degree of the HPP-DMF increases the conditions become less conservative. A numerical example is presented to demonstrate the effectiveness and superiority of the proposed technique.

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Dynamic behavior of the discrete‐time double integrator with saturated locally stabilizing linear state feedback laws

Yang

Stoorvogel

Saberi

2012

Intl J Robust & Nonlinear

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SUMMARYThe main contribution of this paper is to completely characterize the dynamic behavior of the discrete‐time double integrator with a saturated locally stabilizing linear state feedback law. In continuous‐time setting, any linear state feedback control law that locally stabilizes the double integrator also globally stabilizes the system in the presence of actuator saturation. In discrete‐time setting, the equivalent of the double integrator does not have the same property. In this paper, we completely characterize the global behavior of saturated locally stabilizing linear state feedback laws for the discrete‐time double integrator. Copyright © 2012 John Wiley & Sons, Ltd.

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Anti-windup design with guaranteed regions of stability for discrete-time linear systems

Cited by 17 publications

References 15 publications

H∞ control of multiple model subject to actuator saturation: application to quarter-car suspension system

H∞ control of multiple model subject to actuator saturation: application to quarter-car suspension system

Gain Scheduled State Feedback Control for Discrete-Time-Varying Polytopic Systems Subject to Input Saturation

Dynamic behavior of the discrete‐time double integrator with saturated locally stabilizing linear state feedback laws

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