A discrete delay decomposition approach to stability of linear retarded and neutral systems

This paper is concerned with stability of linear time-delay systems of both retarded and neutral types by using some new simple quadratic Lyapunov–Krasovskii functionals. These Lyapunov–Krasovskii functionals consist of two parts. One part comes from some existing Lyapunov–Krasovskii functionals employed in [Han, Q.-L. (2005a). Absolute stability of time-delay systems with sector-bounded nonlinearity. Automatica, 41, 2171–2176; Han, Q.-L. (2005b). A new delay-dependent stability criterion for linear neutral systems with norm-bounded uncertainties in all system matrices. International Journal of Systems Science, 36, 469–475]. The other part is constructed by uniformly dividing the discrete delay interval into multiple segments and choosing proper functionals with different weighted matrices corresponding to different segments. Then using these new simple quadratic Lyapunov–Krasovskii functionals, some new discrete delay-dependent stability criteria are derived for both retarded systems and neutral systems. It is shown that these criteria for retarded systems and neutral systems are always less conservative than the ones in Han (2005a) and Han (2005b) cited above, respectively. Numerical examples also show that the results obtained in this paper significantly improve the estimate of the discrete delay limit for stability over some other existing results.