Robust Delay Dependent Stability Analysis of Neutral Systems
This chapter focuses on the delay-dependent robust stability of linear neutral delay systems. The systems under consideration are described by functional differential equations, with norm bounded time varying nonlinear uncertainties in the “state”, in the delayed “state” and norm bounded time varing quasilinear uncertainties in the difference operator. Two unknown constant delays, in the delayed “stale” and in the difference operator, lead to consider a more general delay-dependent robust stability problem. The analysis is performed via Lyapunov-Krasovskii functional approach. The main difference with respect to 18 is that we obtain sufficient conditions for robust stability given in tenns of the existence of positive dcfinite solutions of LMIs. Thc proposed stability analysis extends some previous results on the subject.
KeywordsRobust Stability Functional Differential Equation Time Delay System Neutral System Neutral Functional Differential Equation
Unable to display preview. Download preview PDF.
- 2.Boyd S., L.EI Ghaoui, E. Feron and V. Balakrishnan (1994) Linear Matrix Inequalities in System and Control Theory. Society for Industrial and Applied Mathematics.Google Scholar
- 4.Bums J. A. Herdman T.L and Stech H.W (1983) Linear Functional Differential Equations As Semigroups On Products Spaces. SIAM. J. Math. Anal., 14:98–116.Google Scholar
- 7.Diekmann O., S.A. van Gils, S.M. Verduyn Lunel and H.-O. Waither (1995). Delay Equations Functional-, Complex-, and Nonlinear Analysis. Springer Verlag.Google Scholar
- 9.Hale J.K. and S.M. Verduyn Lunel (1993) Introduction to Functional Differential Equations. Springer-Verlag.Google Scholar
- 12.Kharitonov V.L. (1998) Robust Stability Analysis of lime-Delay Systems; a survey. Proc. IFAC Syst. Struct. & Contr., Nantes, France:1–12.Google Scholar
- 14.Kolmanovskii V.B. and A.D. Myshkis (1999) Introduction to the Theory and Applications of Functional Differential Equations. Kluwer Academic Publishers.Google Scholar
- 15.Kolmanovskii V.B. and J.P. Richard (1998) Stability of systems with pure, discrete multi-delays. IFAC Conference System Structure and Control Nantes, France: 13–18.Google Scholar
- 17.Rodriguez S.A., J.M. Dion, L. Dugard and D. Ivănescu (2001) On delay-dependcnt robust stability of neutral systems. 3rd IFAC Workshop on Time Delay Systems, Santa Fe USA: 101–106.Google Scholar
- 18.Rodriguez S.A., J.M. Dion and L. Dugard. (2002) Robust Stability Analysis of Neutral Systems Under Model Transformation. 41st IEEE Conference on Decision and Control, Las Vegas, Nevada, USA: 1850–1855.Google Scholar
- 19.Verriest E.I. and S.I. Niculescu (1997) Delay-Independent Stability of LNS: A Riccati Equation Approach, in Stability and Control of Time-Delay Systems. (L. Dugard and E.I. Verriest, Eds.), Springer-Verlag L 228:92–100.Google Scholar