Passivity and complementarity

Camlibel, M. Kanat; Iannelli, Luigi; Vasca, Francesco

doi:10.1007/s10107-013-0678-4

Cited by 30 publications

(30 citation statements)

References 32 publications

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“…, see for instance Chapter 3 in [30]. One may also define the passivity with a positive semidefinite P. Then if the pair (C, A) is observable it follows that the solutions of the LMI Q ≤ 0 are full-rank, hence P is positive definite [31]. Definition 2.…”

Section: Dissipativity and Stability Resultsmentioning

confidence: 99%

Well-posedness, stability and invariance results for a class of multivalued Lur’e dynamical systems

Brogliato

Goeleven

2011

Nonlinear Analysis: Theory, Methods & Applications

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This paper analyzes the existence and uniqueness issues in a class of multivalued Lur'e systems, where the multivalued part is represented as the subdifferential of some convex, proper, lower semicontinuous function. Through suitable transformations the system is recast into the framework of dynamic variational inequalities and the well-posedness (existence and uniqueness of solutions) is proved. Stability and invariance results are also studied, together with the property of continuous dependence on the initial conditions. The problem is motivated by practical applications in electrical circuits containing electronic devices with nonsmooth multivalued voltage/current characteristics, and by state observer design for multivalued systems.

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Section: Dissipativity and Stability Resultsmentioning

confidence: 99%

Well-posedness, stability and invariance results for a class of multivalued Lur’e dynamical systems

Brogliato

Goeleven

2011

Nonlinear Analysis: Theory, Methods & Applications

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“…Linear time-invariant systems together with static relations described by set-valued mappings have been used extensively. An incomplete inventory includes electrical networks with switching elements as in power converters [12][13][14][15][16], linear relay systems [17,18], piecewise linear systems [19], and projected dynamical systems [20,21]; see also [22][23][24] for further examples and [25,26] for numerical analysis of maximal monotone differential inclusions.…”

Section: Introductionmentioning

confidence: 99%

Linear passive systems and maximal monotone mappings

Camlibel

Schumacher

2015

Math. Program.

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This paper deals with a class of dynamical systems obtained from interconnecting linear systems with static set-valued relations. We first show that such an interconnection can be described by a differential inclusions with a maximal monotone set-valued mappings when the underlying linear system is passive and the static relation is maximal monotone. Based on the classical results on such differential inclusions, we conclude that such interconnections are well-posed in the sense of existence and uniqueness of solutions. Finally, we investigate conditions which guarantee well-posedness but are weaker than passivity. Mathematics Subject Classification

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“…Hx, H r x r η y = He + J η with ( A, G, H, J), and is hence negative-semidefinite. Thus, the matrix J is positive semidefinite and ker(J + J ) ⊆ ker(P G − H ), see [12] for proof. All the remaining hypothesis of Theorem 1 hold by construction, and hence the closed-loop system has a unique solution.…”

Section: Regulation With State Feedbackmentioning

confidence: 99%

Well-Posedness and Output Regulation for Implicit Time-Varying Evolution Variational Inequalities

Tanwani¹,

Brogliato²,

Prieur³

2018

SIAM J. Control Optim.

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A class of evolution variational inequalities (EVIs), which comprises ordinary differential equations (ODEs) coupled with variational inequalities (VIs) associated with time-varying set-valued mappings, is proposed in this paper. We first study the conditions for existence and uniqueness of solutions. The central idea behind the proof is to rewrite the system dynamics as a differential inclusion which can be decomposed into a single-valued Lipschitz map, and a time-dependent maximal monotone operator. Regularity assumptions on the set-valued mapping determine the regularity of the resulting solutions. Complementarity systems with time-dependence are studied as a particular case. We then use this result to study the problem of designing state feedback control laws for output regulation in systems described by EVIs. The derivation of control laws for output regulation is based on the use of internal model principle, and two cases are treated: First, a static feedback control law is derived when full state feedback is available; In the second case, only the error to be regulated is assumed to be available for measurement and a dynamic compensator is designed. As applications, we demonstrate how control input resulting from the solution of a variational inequality results in regulating the output of the system while maintaining polyhedral state constraints. Another application is seen in designing control inputs for regulation in power converters.

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Passivity and complementarity

Cited by 30 publications

References 32 publications

Well-posedness, stability and invariance results for a class of multivalued Lur’e dynamical systems

Well-posedness, stability and invariance results for a class of multivalued Lur’e dynamical systems

Linear passive systems and maximal monotone mappings

Well-Posedness and Output Regulation for Implicit Time-Varying Evolution Variational Inequalities

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