Abstract
This paper is concerned with the problem of stability analysis for systems with additive time-varying delays (ATDs). This paper proposes a new free-matrix-based integral inequality that provides estimate of the energy of the vector that contains the state and its derivative at the same time. Consequently, the proposed inequality enables the Lyapunov-Krasovskii functional (LKF) to take into account not only the respective energies of the state and its derivatives but also the correlated effect of them. Then, based on the proposed inequality, this paper derives a new stability criterion of systems with ATDs. This paper constructs LKF by proposing new sets of multiple subintervals of the ATDs, and makes use of the proposed inequality when estimating the derivatives of the LKF. This allows the resulting stability criterion to take full advantage of the information of the multiple subintervals of the ATDs. This paper also successfully applies the proposed free-matrix-based integral inequality to the system with a single time-varying delay. Three numerical examples demonstrate the effectiveness of the proposed methods.
Highlights
In practical world, there exist many dynamical systems whose future evolution depends on their present state and on their past states
Most of the studies on the stability analysis of system with time delays have focused on searching a maximum upper bound of the time delay (MUBTD) satisfying asymptotic stability of the system based on the Lyapunov stability theory
This paper dealt with the problem of stability analysis for systems with additive time-varying delays (ATDs)
Summary
There exist many dynamical systems whose future evolution depends on their present state and on their past states. Motivated by the above discussion, this paper considers the problem of stability analysis for systems with ATDs. This paper proposes a new free-matrix-based integral inequality that provides estimate of the energy of the vector that contains the state and its derivative at the same time. This paper constructs LKF by proposing new sets of multiple subintervals of the ATDs, and makes use of the proposed inequality when estimating the derivatives of the LKF This allows the resulting stability criterion to take full advantage of the information of the multiple subintervals of the ATDs. This paper applies the proposed free-matrix-based integral inequality to the system with a single time-varying delay.
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