Piecewise Linear Modeling and Analysis

Leenaerts, D.M.W.; Bokhoven, Wim M. Van

doi:10.1007/978-1-4757-6190-0

Cited by 138 publications

(89 citation statements)

References 47 publications

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“…Their aim was to compute the steady-state of piecewise linear circuit by means of the complementarity models. See the book [36] for a good account. The notion of solution was extremely clear since it reduces to the question of the existence and possible uniqueness of solutions as a vector, say x, in a finite-dimensional space, say R n .…”

Section: Solution Concepts and Well-posedness For Complementarity Sysmentioning

confidence: 99%

“…Following [36], let us consider the Sah model of the nMOSFET (n metal-oxidesemiconductor field-effect transistor) static characteristic …”

Section: Nonsmooth Mosfet Transistorsmentioning

confidence: 99%

“…The piecewise and quadratic nature of the function (14.60) is approximated by the following (s + 2)-segment piecewise-linear function [36]: …”

Section: A Piecewise-linear Modelmentioning

confidence: 99%

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Time-Stepping via Complementarity

Acary¹

2012

Advances in Industrial Control

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International audienceIn this chapter, the numerical time integration methods for switched electronic circuits are described with a focus on the event-capturing time-stepping schemes based on the complementarity theory. After briefly introducing the strengths and weaknesses of various simulation approaches (hybrid, regularized and nonsmooth), the mathematical nature of solutions for dynamical complementarity systems are discussed in view of numerical time-integration. Then the formulation of the time-stepping methods via complementarity will be described. For each class of solutions, a suitable method is provided and its properties will be illustrated on simple electrical circuits. Some implementation details will be then explained. Especially, the complementarity solvers that are used at each time-step will be described recalling the main families of available solvers. Some insights on the software implementation will also be given. Finally, numerical applications and examples on more realistic circuits will be considered. We will mainly focus on the architecture of a power converter: the Buck converter

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Section: Solution Concepts and Well-posedness For Complementarity Sysmentioning

confidence: 99%

“…Following [36], let us consider the Sah model of the nMOSFET (n metal-oxidesemiconductor field-effect transistor) static characteristic …”

Section: Nonsmooth Mosfet Transistorsmentioning

confidence: 99%

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Time-Stepping via Complementarity

Acary¹

2012

Advances in Industrial Control

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“…Such representation can be considered really general for describing set-valued piecewise linear mappings [12]. It is extremely useful also for describing the feedback structure of Figure 1.…”

Section: Preliminariesmentioning

confidence: 99%

Complementarity and passivity for piecewise linear feedback systems

Iannelli

Vasca

Camlibel

2006

Proceedings of the 45th IEEE Conference on Decision and Control

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Abstract-Piecewise linear feedback systems composed by a dynamical linear time invariant system closed in feedback through a static piecewise linear mapping are considered. By representing the closed loop system in the affine complementarity form, passivity is exploited in order to prove existence of absolute continuous solutions and stability of the equilibria. Assuming passivity of the open loop system and using results on equivalent circuit representations of piecewise linear mappings, conditions on the static feedback connection for preserving passivity in closed loop, are proposed and discussed.

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“…[2], [7], [?]. In many situations such an approach is justified from physical principles; however, in many others modelling in state-space form is not justifiable or advisable; see [9], [10], [18] for an elaboration of this viewpoint.…”

Section: Introductionmentioning

confidence: 99%

Autonomy, forward non-Zenoness and quadratic stability of bimodal higher-order piecewise linear systems

Rapisarda

Camlibel

2014

53rd IEEE Conference on Decision and Control

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Abstract-We introduce bimodal higher-order piecewise linear systems, i.e. the sets of solutions of two n-th order linear differential equations with n ≥ 1, coupled with an inequality constraint defined by a polynomial differential operator acting on the system trajectories. Under suitable assumptions on the characteristic polynomials of the differential equations and the polynomial associated with the inequality constraint, we prove that a solution always exists and is unique given the initial conditions, that no forward Zeno-behavior occurs, and that the trajectories are continuous together with their first n − 1 derivatives. Moreover, we prove that such systems are quadratically stable, and we provide an algorithm based on polynomial algebra to compute a Lyapunov function.

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Piecewise Linear Modeling and Analysis

Cited by 138 publications

References 47 publications

Time-Stepping via Complementarity

Time-Stepping via Complementarity

Complementarity and passivity for piecewise linear feedback systems

Autonomy, forward non-Zenoness and quadratic stability of bimodal higher-order piecewise linear systems

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