Stability of bilinear sampled-data systems with an emulation of static state feedback

Omran, Hassan; Hetel, Laurentiu; Richard, Jean‐Pierre; Lamnabhi‐Lagarrigue, Françoise

doi:10.1109/cdc.2012.6426206

Cited by 5 publications

(3 citation statements)

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“…whereŨ := U 0 0 0 , λ > 0 and P 0 , Q, R, S, U are symmetric positive definite matrices. Using such particular forms of Lyapunov functions, LMI stability conditions have been derived in the literature [120,187,195,205,92,65]. We point in particular to the term (51) used in [187] which provided a significant improvement in what concerns the conservatism reduction.…”

Section: Numerically Tractable Stability Criteriamentioning

confidence: 99%

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Recent developments on the stability of systems with aperiodic sampling: An overview

et al. 2017

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International audienceThis article presents basic concepts and recent research directions about the stability of sampled-data systems with aperiodic sampling. We focus mainly on the stability problem for systems with arbitrary time-varying sampling intervals which has been addressed in several areas of research in Control Theory. Systems with aperiodic sampling can be seen as time-delay systems, hybrid systems, Input/Output interconnections, discrete-time systems with time-varying parameters, etc. The goal of the article is to provide a structural overview of the progress made on the stability analysis problem. Without being exhaustive, which would be neither possible nor useful, we try to bring together results from diverse communities and present them in a unified manner. For each of the existing approaches, the basic concepts, fundamental results, converse stability theorems (when available), and relations with the other approaches are discussed in detail. Results concerning extensions of Lyapunov and frequency domain methods for systems with aperiodic sampling are recalled, as they allow to derive constructive stability conditions. Furthermore, numerical criteria are presented while indicating the sources of conservatism, the problems that remain open and the possible directions of improvement. At last, some emerging research directions, such as the design of stabilizing sampling sequences, are briefly discussed

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Section: Numerically Tractable Stability Criteriamentioning

confidence: 99%

“…It is applicable for both constant and variable sampling intervals. For a constructive application to the case of bilinear systems see [205]. A numerical formulation using Sum-of-Squares [222] has also been provided in [22].…”

Section: An Estimation Of the Msi For Nonlinear Systemsmentioning

confidence: 99%

Recent developments on the stability of systems with aperiodic sampling: An overview

et al. 2017

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“…For nonlinear systems, the L p -stability properties have been studied in the more general context of networked control systems (NCS) [61]. See also [12], [62], [67], for a particularization to the sampled-data case.…”

Section: B Hybrid System Approachmentioning

confidence: 99%