Stability and passivity analysis of higher‐order differential systems inspired by RLC circuits

• Published in: International journal of circuit theory and applications Vol. 52; no. 3; pp. 1384 - 1398
• Main Authors: Ateş, Muzaffer, Ateş, Muhammet
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.03.2024
• Subjects: Aging (natural); Circuit design; Circuits; Dynamical systems; fourth‐order system; Liapunov direct method; Liapunov functions; Lyapunov stability; Lyapunov's linearization method; Mathematical analysis; passivity; RLC circuit; RLC circuits; Stability analysis; System theory; Systems analysis; Systems theory
• ISSN: 0098-9886; 1097-007X
• DOI: 10.1002/cta.3799

Summary This paper discusses the global asymptotic stability and strong passivity analysis of fourth‐order nonlinear and time‐varying dynamical systems by utilizing the Lyapunov direct method. The mathematical model of the main system is obtained from a non‐linear and aging RLC circuit that we have designed before. RLC circuits play an excellent role in the stability of modern system theory. Without the concept of storage elements, the construction of Lyapunov or energy functions for nonlinear and time‐varying systems may be difficult. Because of this, although there are many studies on the stability concept, but the subject has not been completed yet. Therefore, this study may present some mathematical technicalities to the Lyapunov stability with physical considerations. The Lyapunov functions obtained from RLC circuits are natural storage functions, and they satisfy the dissipation inequality. The theoretical stability results of the system are also discussed by Lyapunov's linearization method. The relationship between stability and passivity is also given. Meanwhile, we realized that linear system analysis is not a guaranteed way for determining the stability properties of a full system. Finally, the correctness and availability of the proposed approach are verified through simulation results. This paper addresses the global asymptotic stability and strong passivity analysis of fourth‐order nonlinear and time‐varying dynamical systems by utilizing the Lyapunov direct method. The mathematical model of the main system is obtained from a non‐linear and aging RLC circuit. RLC circuits play an excellent role in the stability of modern system theory since they provide suitable stability properties.