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This research addresses the problem of globally stabilizing a distinct category of fractional-order power systems (F-OP) by employing an observer-based methodology. To address the inherent nonlinearity in these systems, we leverage a Takagi–Sugeno (TS) fuzzy model. The practical stability of the proposed system is systematically established through the application of a sum-of-squares (SOS) approach. To demonstrate the robustness and effectiveness of our approach, we conduct simulations of the power system using SOSTOOLS v3.00. Our study contributes to advancing the understanding of F-OP and provides a practical framework for their global stabilization. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper investigates both fault estimation and fault-tolerant control problems for polynomial systems with state delay in presence of faults. Before studying the control problem, a polynomial observer is proposed to jointly estimate state and fault vectors. Based on the obtained informations, a polynomial controller is designed to compensate fault effects and to stabilize the closed-loop systems even in presence of state delay. The existence of both polynomial observer and controller is proved via satisfying sufficient conditions based on a sum of square (SOS) approach. Polynomial observer and controller gains are computed using SOSTOOLS. Finally, a numerical example is given to demonstrate that the SOS approach provides a significant improvement in reaction to fault occurrence for time delay systems. Furthermore, a tunnel diode circuit and a mass–spring–damper system are used to illustrate the applicability of the design method. [ABSTRACT FROM AUTHOR]

This paper focuses on the stability and stabilization of polynomial fuzzy systems with time delay. This study is based on a polynomial Lyapunov-Krasovskii functional, and delay-dependent results are described in terms of bilinear sum of squares (SOS) conditions. Two techniques are presented, in this paper, to solve the problem of non-convexity of SOS stability and stabilization conditions for polynomial fuzzy systems with time delay. The first technique presents the SOS stability conditions for a specific class of polynomial fuzzy systems with time delay. Delay-dependent conditions are derived throughout a predefined set of indices. This technique improves delay-independent results existing in the literature. The second method transforms the design problem on an optimization problem subject to SOS constraints. The proposed SOS approach is more innovative and effective than the existing linear matrix inequality in terms of conservatism reduction. The new convex conditions for polynomial fuzzy systems with time delay are shown in terms of SOS which can be solved via SOSTOOLS software. Numerical examples are given to show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]