Fractional output stabilization for a class of bilinear distributed systems

Zitane, Hanaa; Larhrissi, Rachid; Boutoulout, Ali

doi:10.1007/s12215-019-00429-w

Cited by 11 publications

(1 citation statement)

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“…In 2018, the notion of regional stability was introduced for fractional systems in [27], where the authors study the Mittag-Leffler stability and the stabilization of systems with Caputo derivatives, but only on a sub-region of its geometrical domain. More recently, fractional output stabilization problems for distributed systems in the Riemann-Liouville sense were studied [28][29][30], where feedback controls, which ensure exponential, strong, and weak stabilization of the state fractional spatial derivatives, with real and complex orders, are characterized. An analysis of the literature shows that existing results on stability of fractional systems are essentially limited to finite-dimensional fractional order linear systems, while results on infinite-dimensional spaces are a rarity.…”

Section: Introductionmentioning

confidence: 99%

The Stability and Stabilization of Infinite Dimensional Caputo-Time Fractional Differential Linear Systems

2020

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We investigate the stability and stabilization concepts for infinite dimensional time fractional differential linear systems in Hilbert spaces with Caputo derivatives. Firstly, based on a family of operators generated by strongly continuous semigroups and on a probability density function, we provide sufficient and necessary conditions for the exponential stability of the considered class of systems. Then, by assuming that the system dynamics is symmetric and uniformly elliptic and by using the properties of the Mittag-Leffler function, we provide sufficient conditions that ensure strong stability. Finally, we characterize an explicit feedback control that guarantees the strong stabilization of a controlled Caputo time fractional linear system through a decomposition approach. Some examples are presented that illustrate the effectiveness of our results.

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