Incremental ℒ&lt;inf&gt;2&lt;/inf&gt;-gain analysis of piecewise-affine systems using piecewise quadratic storage functions

Waitman, Sérgio; Massioni, Paolo; Bako, Laurent; Scorletti, Gérard; Fromion, Vincent

doi:10.1109/cdc.2016.7798451

Cited by 12 publications

(12 citation statements)

References 18 publications

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“…This paper extends the preliminary results presented in [32], where piecewise-quadratic storage functions were considered. We show that our results are more general than those in [30,21,32], and thus potentially less conservative.…”

Section: Introductionsupporting

confidence: 76%

Incremental L2-gain stability of piecewise-affine systems with piecewise-polynomial storage functions

et al. 2019

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This paper concerns the incremental L2-gain stability of piecewise-affine (PWA) systems. We propose sufficient conditions derived from dissipativity theory to compute an upper bound on the incremental L2-gain. This is achieved by constructing piecewise-polynomial storage functions through the use of sum of squares (SOS) relaxations. The constraints are expressed as linear matrix inequalities (LMIs), which can be solved numerically in an efficient way. The proposed conditions are verified to be less conservative than previous results found in the literature by means of a numerical example.

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Section: Introductionsupporting

confidence: 76%

Incremental L2-gain stability of piecewise-affine systems with piecewise-polynomial storage functions

et al. 2019

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“…They are therefore more easily amenable to interpretation and analysis by judiciously using the available knowledge on linear systems. PWA models can be viewed as a means to extend somehow generically linear design and analysis methods to nonlinear dynamic systems [17], [16]. This is probably one of the reason why there has been recently an increase of interest in piecewise affine models identification from input-output data.…”

Section: Introductionmentioning

confidence: 99%

Piecewise Affine System identification: A least harmonic mean approach

Bako

Yahya

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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In this paper we consider the problem of identifying piecewise affine approximations of nonlinear dynamic systems directly from input-output measurements. This requires estimating a partition of the regression space and an associated set of affine time-invariant models. By relying on a generic Voronoi type of partition, the proposed approach treats these two tasks jointly via the minimization of an appropriate objective function formed as a weighted sum of errors related to all submodels. We minimize this objective function with respect to both the weights and the parameters (describing the partition and the affine submodels) under some heuristic constraint on the weights. It is later observed that the proposed method attempts indeed to optimize a sum (over the available dataset) of harmonic means. The final estimation algorithm consists in solving iteratively a sequence of convex optimization problems. Numerical experiments tend to suggest that the new method exhibits some nice properties: regular convergence and good estimation performance.

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“…In order to obtain less conservative conditions, a piecewise quadratic Lyapunov function is employed. The basic assumption of this technique is the continuity of the partitioned quadratic Lyapunov function on different polyhedrons on the shared boundary [28,29]. Based on Iervolino et al, [30] also proposes a piecewise quadratic Lyapunov function that is not necessarily continuous.…”

Section: Introductionmentioning

confidence: 99%

Robust sampling‐based switching design for piecewise affine systems with application to DC–DC converters

Wang

Liu

Wang

et al. 2019

IET Control Theory & Applications

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Incremental ℒ<inf>2</inf>-gain analysis of piecewise-affine systems using piecewise quadratic storage functions

Cited by 12 publications

References 18 publications

Incremental L2-gain stability of piecewise-affine systems with piecewise-polynomial storage functions

Incremental L2-gain stability of piecewise-affine systems with piecewise-polynomial storage functions

Piecewise Affine System identification: A least harmonic mean approach

Robust sampling‐based switching design for piecewise affine systems with application to DC–DC converters

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