Polynomial-Type Lyapunov–Krasovskii Functional and Jacobi–Bessel Inequality: Further Results on Stability Analysis of Time-Delay Systems
Yibo Huang, Yong He, Jianqi An, Min Wu
Abstract
To derive a less conservative stability criterion via Lyapunov-Krasovskii functional (LKF) method, in previous literature, multiple integral terms are usually introduced into the construction of LKFs. This article generalizes the results of previous literature by proposing a polynomial-type LKF, which contains the LKFs with multiple integral terms as special cases. In addition, a Jacobi-Bessel inequality is presented to bound the derivative of such LKF. As a result, an improved stability criterion of time-delay systems is established. Finally, two numerical examples are given to illustrate the effectiveness, and advantages of our method.
Topics & Concepts
MathematicsBessel functionStability (learning theory)PolynomialType (biology)Applied mathematicsStability criterionDerivative (finance)Mathematical analysisComputer scienceMachine learningDiscrete time and continuous timeEconomicsFinancial economicsEcologyStatisticsBiologyStability and Control of Uncertain SystemsStability and Controllability of Differential EquationsNumerical methods for differential equations