Improved Stability Criteria For Systems With Two Additive Time-varying Delays Via Integral Inequalities

Many practical problems can be expressed in terms of time-varying delay dynamical systems.The stability of time-varying delay dynamical systems is one of the current research hot topics.This paper is concerned with the stability analysis of systems with two additive time-varying delays(TATDs).The main contents of this paper are as follows:In Chapter 1,firstly,we give the background,significance and research methods of the problem.Secondly,the integral inequalities and main lemmas required in this paper are stated.Finally,the main research works of this paper are introduced.In Chapter 2,firstly,we introduce the integral inequality and lemmas needed in this chapter.Secondly,a new linear matrix inequalities(LMIs)framework is formed by combining the auxiliary function-based single integral inequality with the extended reciprocally convex matrix inequality,and a new stability criterion of systems with TATDs is proposed.Finally,because Park et al.construct a new Lyapunov-Krasovskill functions(LKFs)after division of the delay interval,we make use of the auxiliary function-based single integral inequality when estimating the derivatives of the LKFs,obtain an improved stability criterion of systems with TATDs.In Chapter 3,firstly,we introduce the integral inequalities and lemmas needed in this chapter.Then we prove the double integral inequalities can obtain tighter lower bound for the integral terms of the derivatives of LKFs than the Wirtinger-based integral inequality.Secondly,we estimate the derivatives integral terms of LKFs combining the auxiliary function-based double integral inequality with the reciprocally convex matrix inequality,the improved stability criterion of systems with TATDs is proposed in terms of LMIs framework.Finally,we use the generalized multiple-integral inequality to estimate the integral terms of the derivatives of LKFs,obtain an improved stability criterion of systems with TATDs.In Chapter 4,firstly,we introduce the integral inequalities and lemmas needed in this chapter.Compared with the Wirtinger-based integral inequality,the Bessel-Legendre integral inequality and the generalized free matrix inequality can obtain tight lower bound for the integral term of the derivative of LKFs.Secondly,combining the Bessel-Legendre integral inequality with the extended reciprocally convex matrix inequality,a less conservative stability criterion of systems with TATDs is obtained.Finally,the derivative integral terms of LKFs are estimated by using the generalized free matrix inequality,and obtain a new stability criterion of systems with TATDs.