Sufficient linear matrix inequality conditions are given for robust stability analysis of linear uncertain neutral systems, where it is assumed that the vector of states has time-varying delays. All system matrices are supposed to be time invariant, uncertain but belonging to a polytope with known vertices. The robust stability of the uncertain neutral system is assured by means of a parameter dependent Lyapunov-Krasovskii functional. Additionally, it is shown how robust stability conditions for uncertain continuous-time systems with and without state delays can be recovered from the conditions proposed in the paper. Numerical examples illustrate the obtained results.184434446Barmish, B.R., Necessary and sufficient conditions for quadratic stabilizability of an uncertain system (1985) Journal of Optimization Theory and Applications, 46 (4), pp. 399-408Bellen, A., Guglielmi, N. e Ruehli, A. E. (1999). Methods for linear systems of circuit delay differential equations of neutral type, IEEE Transactions on Circuits and Systems Part I: Fundamental Theory and Applications 46(1): 212-216Bin, Y., Ruijun, Z., Tao, L., Delay-dependent stability criterion for a class of neutral time-delay systems (2003) Proceedings of the 2003 American Control Conference, pp. 2694-2696. , Denver, CO, ppBliman, P.-A., Lyapunov equation for the stability of linear delay systems of retarded and neutral type (2002) IEEE Transactions on Automatic Control, 47 (2), pp. 327-335Cao, D.Q., He, P., Stability criteria of linear neutral systems with a single delay (2004) Applied Mathematics and Computation, 148 (1), pp. 135-143Chen, J.-D., New stability criteria for a class of neutral systems with discrete and distributed time-delays: An LMI approach (2003) Applied Mathematics and Computation, 150 (3), pp. 719-736Chen, J.-D., Robust control for uncertain neutral systems with time-delays in state and control input via LMl and GAs (2004) Applied Mathematics and Computation, 157 (2), pp. 535-548Cullum, J., Ruehli, A. e Zhang, T. (2000). A method for reduced-order modeling and simulation of large interconnect circuits and its application to PEED models with retardation, IEEE Transactions on Circuits and Systems Part II: Analog and Digital Signal Processing 47(4): 261-273de Oliveira, M.C., Bernussou, J., Geromel, J.C., A new discrete-time robust stability condition (1999) Systems & Control Letters, 37 (4), pp. 261-265de Oliveira, M.C., Skelton, R.E., Stability tests for constrained linear systems (2001) Lecture Notes in Control and Information Science, 268, pp. 241-257. , S. O. Reza Moheimani ed, Perspectives in Robust Control, of, Springer-Verlag, New York, ppDugard, L., Verriest, E.I., (1997) Stability and Control of Time-delay Systems, , Springer-Verlag, Berlin, GermanyEl'sgol'ts, L.E., (1966) Introduction to the theory of differential equations with deviating arguments, , Holden-Day, Inc, San Francisco, USAFridman, E., New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems (2001) Systems & Control Letters, 43 (4), pp. 309-319Fu, X., Controllability of abstract neutral functional differential systems with unbounded delay (2004) Applied Mathematics and Computation, 151 (2), pp. 299-314Gahinet, P., Nemirovskii, A., Laub, A.J., Chilali, M., (1995) LMI Control Toolbox User's Guide, , The Math Works Inc, Natick, MAGu, K., Kharitonov, V.L., Chen, J., (2003) Stability of Time-delay Systems, Control Engineering, , Birkhäuser, Boston, MAGu, K., Niculescu, S., Survey on recent results in the stability and control of time-delay systems (2003) Journal of Dynamic Systems, Measurement and Control - Transactions of ASME, 125, pp. 125-165Gu, K., Niculescu, S.-I., Further remarks on additional dynamics in various model transformations of linear delay systems (2001) IEEE Transactions on Automatic Control, 46 (3), pp. 497-500Hale, J., (1977) Theory of Functional Differential Equations, , Springer-Verlag, New YorkHale, J., Lunel, S.M.V., (1993) Introduction to Functional Differential Equations, , Springer-Verlag, New YorkHan, Q.-L., Robust stability of uncertain delay-differential systems of neutral type (2002) Automatica, 38 (4), pp. 719-723Han, Q.-L., A descriptor system approach to robust stability of uncertain neutral system with discrete and distributed delays (2004) Automatica, 40 (10), pp. 1791-1796Ivǎnescu, D., Niculescu, S.-I., Dugard, L., Dion, J.-M., Verriest, E.I., On delay-dependent stability for linear neutral systems (2003) Automatica, 39 (2), pp. 255-261Kao, C.-Y., Rantzer, A., Stability criteria for systems with bounded uncertain time-varying delay (2003) Proceedings of the 2003 European Control Conference, , Cambridge, UKKolmanovskii, V.B., Niculescu, S.I., Richard, J.P., On the Liapunov-Krasovskii functionals for stability analysis of linear delay systems (1999) International Journal of Control, 72 (4), pp. 374-384Kolmanovskii, V.B., Richard, J.P., Stability of some linear systems with delays (1999) IEEE Transactions on Automatic Control, 44 (5), pp. 984-989Kolmanovskii, V., Myshkis, A., (1992) Applied Theory of Functional Differential Equations, , Kluwer Academic Publishers, DordrechtKolmanovskii, V., Myshkis, A., (1998) Introduction to the Theory and Applications of Functional Differential Equations, , Kluwer Academic Publishers, DordrechtLeite, V.J.S., Montagner, V.F., de Oliveira, P.J., Oliveira, R.C.L.F., Ramos, D.C.W., Peres, P.L.D., Estabilidade robusta de sistemas lineares através de desigualdades matriciais lineares (2004) SBA Controle & Automação, 15 (1), pp. 24-40Leite, V.J.S., Peres, P.L.D., An improved LMI condition for robust D-stability of uncertain polytopic systems (2003) IEEE Transactions on Automatic Control, 48 (3), pp. 500-504Leite, V. J. S., Peres, P. L. D. e Tarbouriech, S. (2003). Less conservative time-delay independent LMI conditions for continuous-time polytopic systems, Proceedings of the 4th IFAC International Workshop on Linear Time Delay Systems, Rocquencourt, France, in CD-romMahmoud, M.S., Robust Control and Filtering for Time-Delay Systems (2000) Control Engineering Series, , Marcel Dekker, Inc, New YorkMalek-Zavarei, M., Jamshidi, M., (1987) Time-Delay Systems: Analysis, Optimization and Applications, , North-Holland, Amsterdam, The NetherlandsNiculescu, S.-I., Delay Effects on Stability: A Robust Control Approach (2001) Lecture Notes in Control and Information Sciences, 269. , of, Springer-Verlag, LondonPark, J.-H., A new delay-dependent criterion for neutral systems with multiple delays (2001) Journal of Computational and Applied Mathematics, 136 (1-2), pp. 177-184Park, J.H., Simple criterion fot asymptotic stability of interval neutral delay-differential systems (2003) Applied Mathematics Letters, 16 (7), pp. 1063-1068Park, J.H., Kwon, O., Won, S., LMI approach to robust H∞ filtering for neutral delay differential systems (2004) Applied Mathematics and Computation, 150 (1), pp. 235-244Park, J.H., Won, S., Stability analysis for neutral delay-differential systems (2000) Journal of The Franklin Institute, 337 (1), pp. 1-9Peaucelle, D., Arzelier, D., Bachelier, O., Bernussou, J., A new robust Instability condition for real convex polytopic uncertainty (2000) Systems & Control Letters, 40 (1), pp. 21-30Peres, P. L. D., Tarbouriech, S., Garcia, G. e Leite, V. J. S. (2003). Robust stability of time-delay continuous-time systems in polytopic domains, Proceedings of the 2003 European Control Conference, Cambridge, UK. in CD-romRamos, D.C.W., Peres, P.L.D., A less conservative LMI condition for the robust stability of discrete-time uncertain systems (2001) Systems & Control Letters, 43 (5), pp. 371-378Ramos, D.C.W., Peres, P.L.D., An LMI condition for the robust stability of uncertain continuous-time linear systems (2002) IEEE Transactions on Automatic Control, 47 (4), pp. 675-678Richard, J.-P., Time-delay systems: An overview of some recent advances and open problems (2003) Automatica, 39 (10), pp. 1667-1694Skorodinskii, V.I., Iterational method of construction of Lyapunov-Krasovskii functionals for linear systems with delay (1990) Automation and Remote Control, 51 (9), pp. 1205-1212Verriest, E.I., Robust stability and adaptive control of time-varying neutral systems (1999) Proceedings of the 38th IEEE Conference on Decision and Control, pp. 4690-4695. , Phoenix, AZ, ppVieira, A., Kailath, T., On another approach to the Schur-Cohn criterion (1977) IEEE Transactions on Circuits and Systems, CAS-24, pp. 218-220Xu, S., Lam, J., Yang, C., Verriest, E.I., An LMI approach to guaranteed cost control for uncertain linear neutral delay systems (2003) International Journal of Robust and Nonlinear Control, 13 (1), pp. 35-53Yue, D. e Han, Q.-L. (2004). A delay-dependent stability criterion of neutral systems and its application to a partial element equivalent circuit model, IEEE Transactions on Circuits and Systems Part II: Analog and Digital Signal Processing 51(12): 685-689Zhang, J., Knospe, C., Tsiotras, P., Stability of time-delay systems: Equivalence between Lyapunov and scaled small-gain conditions (2001) IEEE Transactions on Automatic Control, 46 (3), pp. 482-486