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

Abstract

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.

Keywords

• fractional-order systems
• caputo derivative
• quasi-one-sided lipschitz condition
• nonlinear systems
• observer design
• output feedback stabilization
• separation principle