SOS Approach for Practical Stabilization of Tempered Fractional-Order Power System

Abstract

Fractional systems have been widely utilized in various fields, such as mathematics, physics and finance, providing a versatile framework for precise measurements and calculations involving partial quantities. This paper aims to develop a novel polynomial controller for a power system (PS) with fractional-order (FO) dynamics. It begins by studying the practical stability of a general class of tempered fractional-order (TFO) nonlinear systems, with broad applicability and potential for expanding its applications. Afterward, a polynomial controller is designed to guarantee the practical stability of the PS, encompassing the standard constant controller as a specific instance. The design conditions for this controller are resolved using the sum of squares (SOS) approach, a powerful technique for guaranteeing stability and control design. To showcase the practical value of the analytical findings, simulations of the PS are conducted utilizing SOSTOOLS.

Keywords

• fractional calculus
• Lyapunov theory
• numerical solutions
• SOSTOOLS
• practical stability