Linear systems with bounded inputs: global stabilization with eigenvalue placement

Suárez, Rodolfo; Daun, J Solis; Ramírez, J.

doi:10.1002/(sici)1099-1239(199709)7:9<835::aid-rnc216>3.3.co;2-g

Cited by 45 publications

(15 citation statements)

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“…Although this work was not anti-windup per se, this line of work provided important theoretical results which anti-windup would later benefit from. Some useful references on this subject are [68,117,88,96] and the survey [4] contains an excellent overview.…”

Section: Historical Developmentmentioning

confidence: 99%

Anti-windup design: an overview of some recent advances and open problems

Tarbouriech

Turner

2009

IET Control Theory Appl.

514

256

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This paper deals with the anti-windup technique which can be used to tackle the problems of stability and performance degradation for linear systems with saturated inputs. The anti-windup techniques which can be found in the literature today have evolved from many sources and, even now, are diverse and somewhat disconnected from one another. In this survey, an overview of many recent anti-windup techniques are provided and their connections to one another are stated. The anti-windup technique is also explained within the context of its historical emergence and the likely future directions of the field are speculated. The focus of this paper is on the so-called "modern" anti-windup techniques which began to emerge during the end of the 20th century and which allow a priori guarantees on stability to be made. The survey attempts to provide constructive LMI conditions for the synthesis of anti-windup compensators in both global and local contexts. Finally, some interesting extensions and open problems are discussed, such as nested saturations, the presence of time delays in the state or the input, and anti-windup for nonlinear systems.

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Section: Historical Developmentmentioning

confidence: 99%

Anti-windup design: an overview of some recent advances and open problems

Tarbouriech

Turner

2009

IET Control Theory Appl.

514

256

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“…On the other hand, control of systems with saturationtype nonlinearities has also been well studied and a lot of results have been reported in the literature (see [9][10][11][12][13][14][15] and the references given there).…”

Section: Introductionmentioning

confidence: 99%

Stabilization of linear systems with input delay and saturation—A parametric Lyapunov equation approach

Zhou

Lin

Duan

2010

Intl J Robust & Nonlinear

103

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SUMMARYThis paper studies the problem of stabilizing a linear system with delayed and saturating feedback. It is known that the eigenstructure assignment-based low-gain feedback law (globally) stabilizes a linear system in the presence of arbitrarily large delay in its input, and semi-globally stabilizes it when the input is also subject to saturation, as long as all its open-loop poles are located in the closed left-half plane. Based on a recently developed parametric Lyapunov equation-based low-gain feedback design method, this paper presents alternative, but simpler and more elegant, feedback laws that solve these problems. The advantages of this new approach include its simplicity, the capability of giving explicit conditions to guarantee the stability of the closed-loop system, and the ease in scheduling the low-gain parameter on line to achieve global stabilization in the presence of actuator saturation.

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“…All that is left is to formulate the implication in (18) more precisely, and apply the S-procedure. The left side of the implication will be the equations in (17), while the right will be a condition on one of our candidate Lyapunov functions in (13)- (14).…”

Section: E Main Resultsmentioning

confidence: 99%

“…(See [15] for a complete derivation of the above constraints). Hence, we will actually verify the truthfulness of the implication Constraints implied by KT conditions in (17) ) Lyapunov function decreasing:…”

Section: Stability As An Implicationmentioning

confidence: 94%

Kuhn-Tucker-based stability conditions for systems with saturation

Primlos

Giannelli

2001

IEEE Trans. Automat. Contr.

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This note presents a new approach to deriving stability conditions for continuous-time linear systems interconnected with a saturation. The method presented here can be extended to handle a deadzone, or in general, nonlinearities in the form of piecewise linear functions. By representing the saturation as a constrained optimization problem, the necessary (Kuhn-Tucker) conditions for optimality are used to derive linear and quadratic constraints which characterize the saturation. After selecting a candidate Lyapunov function, we pose the question of whether the Lyapunov function is decreasing along trajectories of the system as an implication between the necessary conditions derived from the saturation optimization, and the time derivative of the Lyapunov function. This leads to stability conditions in terms of linear matrix inequalities (LMIs), which are obtained by an application of the S-procedure to the implication. An example is provided where the proposed technique is compared and contrasted with previous analysis methods.

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Linear systems with bounded inputs: global stabilization with eigenvalue placement

Cited by 45 publications

References 0 publications

Anti-windup design: an overview of some recent advances and open problems

Anti-windup design: an overview of some recent advances and open problems

Stabilization of linear systems with input delay and saturation—A parametric Lyapunov equation approach

Kuhn-Tucker-based stability conditions for systems with saturation

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