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Practical Mittag-Leffler stability of quasi-one-sided Lipschitz fractional order systems

Basdouri Imed, Kasmi Souad, Lerbet Jean

Archives of Control Sciences

2023

Vol. 33, No. 1

55--70

This paper focuses on the global practical Mittag-Leffler feedback stabilization problem for a class of uncertain fractional-order systems. This class of systems is a larger class of nonlinearities than the Lipschitz ones. Based on the quasi-one-sided Lipschitz condition, firstly, we provide sufficient conditions for the practical observer design. Then, we exhibit that practical Mittag-Leffler stability of the closed loop system with a linear, state feedback is attained. Finally, a separation principle is established and we prove that the closed loop system is practical Mittag-Leffler stable.

Multiobservers and their application to output stabilization

Wyrwas M.

Control and Cybernetics

2006

Vol. 35, no 4

977-995

A construction of multiobserver is extended to arbitrary analytic control systems without any observability property. The dynamics of the multiobserver gives an estimation of the successive derivatives of the output and the output of the multiobserver is a set that approximates the whole class of states that are indistinguishable from the current state of the original system by the control applied to the system. The dynamics of the multiobserver is used to stabilize the system with the aid of output feedback. It is done under the assumption that the system is state-feed back stabilizable and the functions used in this feedback depend smoothly on the output function and its Lie derivatives.