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Exponential stability of nonlinear neutral systems with time-varying delay

In this paper, the problem of exponential stability for a class of nonlinear neutral systems with interval time-varying delay is studied. Based on improved Lyapunov-Krasovskii functionals combine with Leibniz-Newton’s formula, new delay-dependent sufficient conditions for the exponential stability of the systems are established in terms of linear matrix inequalities (LMIs), which allows to compute the maximal bound of the exponential stability rate of the solution. | JOURNAL OF SCIENCE OF HNUE Natural Sci. 2013 Vol. 00 No. 0 pp. 1-11 Exponential stability of nonlinear neutral systems with time-varying delay Le Van Hien and Hoang Van Thi Hanoi National University of Education Hong Duc University Thanh Hoa E-mail Hienlv@hnue.edu.vn Abstract. In this paper the problem of exponential stability for a class of nonlin- ear neutral systems with interval time-varying delay is studied. Based on im- proved Lyapunov-Krasovskii functionals combine with Leibniz-Newton s for- mula new delay-dependent sufficient conditions for the exponential stability of the systems are established in terms of linear matrix inequalities LMIs which allows to compute the maximal bound of the exponential stability rate of the solution. Numerical examples are also given to show the effectiveness of the obtained results. Keywords Neutral systems interval time-varying delay nonlinear uncer- tainty exponential stability linear matrix inequality 1. Introduction Time-delay occurs in most of practical models such as aircraft stabilization chemi- cal engineering systems inferred grinding model manual control neural network nuclear reactor population dynamic model ship stabilization and systems with lossless transmis- sion lines. The existence of this time-delay may be the source for instability and bad per- formance of the system. Hence the problem of stability analysis for time-delay systems has received much attention of many researchers in recent years see 4 5 7 11 12 14 17 and references therein. In many practical systems the system models can be described by functional differ- ential equations of neutral type which depend on both state and state derivatives. Neutral system examples include distributed networks heat exchanges and processes involving steam. Recently the stability analysis of neutral systems has been widely investigated by many researchers see 3 7 for time-varying delay and 8 10-12 for interval time- varying delay. The main approach is .