Stability Criteria for Asynchronous Sampled-data Systems – A Fragmentation Approach

Briat, Corentin; Seuret, Alexandre

doi:10.3182/20110828-6-it-1002.02353

Cited by 11 publications

(11 citation statements)

References 24 publications

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“…Let us consider for instance a sampled-data system with matrices [Naghshtabrizi et al, 2008, Seuret, 2012, Briat and Seuret, 2011]…”

Section: Examplesmentioning

confidence: 99%

Robust stability of impulsive systems: A functional-based approach

Briat¹,

Seuret

2012

IFAC Proceedings Volumes

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To cite this version:Corentin Briat, Alexandre Seuret. Abstract: An improved functional-based approach for the stability analysis of linear uncertain impulsive systems relying on Lyapunov looped-functionals is provided. Looped functionals are peculiar functionals that allow to encode discrete-time stability criteria into continuous-time conditions and to consider non-monotonic Lyapunov functions along the trajectories of the impulsive system. Unlike usual discrete-time stability conditions, the obtained ones are convex in the system matrices, an important feature for extending the results to uncertain systems. It is emphasized in the examples that the proposed approach can be applied to a class of systems for which existing approaches are inconclusive, notably systems having unstable continuous and discrete dynamics.

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“…Let us consider for instance a sampled-data system with matrices [Naghshtabrizi et al, 2008, Seuret, 2012, Briat and Seuret, 2011]…”

Section: Examplesmentioning

confidence: 99%

Robust stability of impulsive systems: A functional-based approach

Briat¹,

Seuret

2012

IFAC Proceedings Volumes

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“…Increasing sampling intervals leads to the low channel occupation. Therefore, sampled‐data systems have attracted considerable attention from many researchers …”

Section: Introductionmentioning

confidence: 99%

“…The framework based on the looped functional gives the relaxation of positivity constraints on the looped functional. In the work of Briat and Seuret, a fragmentation approach was proposed, which divides the sampling interval uniformly. In the work of Seuret and Gouaisbaut, Wirtinger‐based integral inequality was applied to the framework based on the looped functional.…”

Section: Introductionmentioning

confidence: 99%

A less conservative stability criterion for sampled‐data system via a fractional‐delayed state and its state‐space model

Park

2019

Intl J Robust & Nonlinear

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Summary This paper introduces a state‐space model based on a fractional‐delayed state for a sampled‐data system described as a linear system under aperiodic sampling intervals. The new state‐space model exploits the information on the sampled‐data system and the fractional‐delayed state, which is defined on the sampling interval. The fractional‐delayed state and its state‐space model are utilized to construct the Lyapunov functional, which consists of the traditional Lyapunov function and a looped functional whose boundary conditions are zeros at sampling instants. Based on the Lyapunov functional, a stability criterion and a robust stability criterion are derived in terms of linear matrix inequalities. Simulation results show the effectiveness of the proposed criterion.

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“…In this regard, the class of looped functional is more flexible than the class of Lyapunov functionals, allowing then the possibility for obtaining less conservative results. They have been successfully applied to the robust stability analysis of sampled‐data systems , impulsive systems , and switched systems . Unlike in the previous papers on impulsive systems where a restrictive class of looped functionals is used, a more general family of functionals, proven to be ‘complete’, is considered here.…”

Section: Introductionmentioning

confidence: 99%

Theoretical and numerical comparisons of looped functionals and clock-dependent Lyapunov functions-The case of periodic and pseudo-periodic systems with impulses

Briat

2015

Int. J. Robust. Nonlinear Control

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Summary The stability of uncertain periodic and pseudo‐periodic systems with impulses is analyzed in the looped‐functional and clock‐dependent Lyapunov function frameworks. These alternative and equivalent ways for characterizing discrete‐time stability have the benefit of leading to stability conditions that are convex in the system matrices, hence suitable for robust stability analysis. These approaches, therefore, circumvent the problem of computing the monodromy matrix associated with the system, which is known to be a major difficulty when the system is uncertain. Convex stabilization conditions using a non‐restrictive class of state‐feedback controllers are also provided. The obtained results readily extend to uncertain impulsive periodic and pseudo‐periodic systems, a generalization of periodic systems that admit changes in the ‘period’ from one pseudo‐period to another. The obtained conditions are expressed as infinite‐dimensional semidefinite programs, which can be solved using recent polynomial programming techniques. Several examples illustrate the approach, and comparative discussions between the different approaches are provided. A major result obtained in the paper is that despite being equivalent, the approach based on looped functional reduces to the one based on clock‐dependent Lyapunov functions when a particular structure for the looped functional is considered. The conclusion is that the approach based on clock‐dependent Lyapunov functions is preferable because of its lower computational complexity and its convenient structure enabling control design. Copyright © 2015 John Wiley & Sons, Ltd.

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Stability Criteria for Asynchronous Sampled-data Systems – A Fragmentation Approach

Cited by 11 publications

References 24 publications

Robust stability of impulsive systems: A functional-based approach

Robust stability of impulsive systems: A functional-based approach

A less conservative stability criterion for sampled‐data system via a fractional‐delayed state and its state‐space model

Theoretical and numerical comparisons of looped functionals and clock-dependent Lyapunov functions-The case of periodic and pseudo-periodic systems with impulses

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