Exponential Stability of Interval Dynamical Systems with Quadratic Nonlinearity

Abstract

This article proposes an approach for investigating the exponential stability of a nonlinear interval dynamical system with the nonlinearity of a quadratic type on the basis of the Lyapunov's direct method. It also constructs an inner estimate of the attraction domain to the origin for the system under consideration.

Stability and Stabilizability Criteria of Nonlinear Interval Systems and Their Application in Electronic Circuits

“…Reviewing the relevant research literatures in the field of interval systems, the most investigated categories are linear systems 9,10,11,12,13,14,15,16,17 , nonlinear systems 18,19,20,21,22,23 , and time-delay systems 21,24 , among which nonlinear systems are suitable for most electronic circuits. For the interval systems under parameter perturbations, stability, especially asymptotic stability, is the most important issue in engineering applications.…”

“…Therefore, the next step is to find the corresponding analysis and controller design methods in this field to provide theoretical and technical support. For the stability and stabilizability of interval systems, the current typical analysis methods include Kharitonov's theorem methods 16 , Lyapunov and Lyapunov-Krasovskii functional (LKF) methods 14,22,23,25 , Edge theorem methods 15 , value set methods 10,17,21 , linear matrix inequality (LMI) methods 9,11,12,13,14,19 , etc. Among the above methodologies, only Lyapunov and LKF methods might obtain criteria with universality of the nonlinear nominal models, which are commonly used for nonlinear systems and time-delay systems, while other methods are mainly suitable for linear systems and only applicable to specific objects without the possibility of extensive application to nonlinear interval systems.…”