The paper is engaged with the framework of designing adaptive fault estimation for linear continuous-time systems with distributed time delay. The Lyapunov-Krasovskii functional principle is enforced by imposing the integral partitioning method and a new equivalent delaydependent design condition for observer-based assessment of faults are established in terms of linear matrix inequalities. Asymptotic stability conditions are derived and regarded with respect to the incidence of structured matrix variables in the linear matrix inequality formulation. Simulation results illustrate the design approach, and demonstrates power and performance of the actuator fault assessment.
 L. BAI, Z. TIAN, S. SHI: Robust fault detection for a class of nonlinear time-delay systems. J. of the Franklin Institute, 344(6), (2007), 873-888.
 Z. FENG, J. LAM: Integral partitioning approach to stability analysis and stabilization of distributed time delay systems. Prep. of the 18th IFAC World Congress, Milano, Italy, (2011), 5094-5099.
 Z. FENG, J. LAM: Integral partitioning approach to robust stabilization for uncertain distributed time delay systems. Int. J. of Robust and Nonlinear Control, 22(6), (2012), 676-689.
 Y.A. FIAGBEDZI, A.E. PEARSON: A multistage reduction technique for feedback stabilizing distributed time-lag systems. Automatica, 23(3), (1987), 311-326.
 A. FILASOVÁ , D. GONTKOVIČ, D. KROKAVEC: LMI based control design for linear systems with distributed time delays. Archives of Control Sciences, 22(2), (2012), 217-231.
 A. FILASOVÁ, D. GONTKOVIČ, D. KROKAVEC: Actuator faults estimation for a class of linear distributed time delay systems. Prep. of the 10th European Workshop on Advanced Control and Diagnosis ACD 2012, Copenhagen-Lyngby, Denmark, (2012), 3.1-3.6.
 M. GIL’: Exponential stability of nonlinear neutral type systems. Archives of Control Sciences, 22(2), (2012), 125-143.
 F. GOUAISBAUT, D. PEAUCELLE: Delay-dependent stability analysis of linear time delay systems. Proc. of the 6th IFACWorkshop on Time Delay System TDS’06, LAquila, Italy, (2006), 54-59.
 K. GU: An integral inequality in the stability problem of time-delay systems. Proc. of the 39th IEEE Conference on Decision and Control, Sydney, Australia, (2000), 2805-2810.
 K. GU: An improved stability criterion for systems with distributed delays. Int. J. of Robust and Nonlinear Control, 13(9), 2003, 819-831.
 B. JIANG, M. STAROSWIECKI, V. COCQUEMPOT: Fault identification for a class of time-delay systems. Proc. of the American Control Conference 2002, Anchorage, AK, USA, (2002), 2239-2244.
 C. JIANG, D.H. ZHOU: Fault detection and identification for uncertain linear neutral delay systems. Proc. of the 16th IFAC World Congress 2005, Prag, Czech Republic, (2005), 1825-1825.
 T. KACZOREK and L. SAJEWSKI: Stability of continuous-discrete linear sys- tems with delays in state vector. Archives of Control Sciences, 21(1), (2011), 25-36.
 N.N. KRASOVSKII: On the application of Lyapunov’s second method for equations with time delays. Prikladnaia Matematika i Mekhanika, 20(2), (1956), 315-327, (in Russian).
 N.N. KRASOVSKII: Stability of Motion. Application of Lyapunov’s Second Method to Differential Systems and Equations with Delay, Standford University Press, Standford, CA, USA, 1963.
 D. KROKAVEC, A. FILASOVÁ: Dynamic Systems Diagnosis. Elfa, Košice, Slovakia, 2007, (in Slovak).
 S.I. NICULESCU, E.I. VERIEST, L. DUGARD, J.M. DION: Stability and robust stability of time-delay systems. A guided tour. Stability and Control of Time-delay Systems, Springer-Verlag, Berlin, (1998), 1-71.
 D. PEAUCELLE, D. HENRION, Y. LABIT, K. TAITZ: User’s Guide for SeDuMi Interface 1.04, LAAS-CNRS, Toulouse, 2002.
 J.P. RICHARD: Time-delay systems: An overview of some recent advances and open problems. Automatica, 39(10), (2003), 1667-1694.
 U. SHAKED, I. YAESH, C.E. DE SOUZA: Bounded real criteria for linear time systems with state-delay. IEEE Trans. on Automatic Control, 43(7), (1998), 1116-1121.
 Y.S. SUH, H.J. KANG, Y.S. RO: Stability condition of distributed delay systems based on an analytic solution to Lyapunov functional equations. Asian J. of Control, 8(1), (2006), 91-96.
 J. SUN, J. CHEN, G. LIU, D. REES: On robust stability of uncertain neutral systems with discrete and distributed delays. Proc. of American Control Conference ACC’09, St. Louis, MO, USA, (2009), 5469-5473.
 H. WANG, S. DALEY: Actuator fault diagnosis. An adaptive observer-based technique. IEEE Trans. on Automatic Control, 41(7), 1996, 1073-1078.
 M. WU, Y. HE, J.J. SHE, G.P. LIU: Delay-dependent criteria for robust stability of time-varying delay systems. Automatica, 40(8), (2004), 1435-1439.
 F. ZHENG, P.M. FRANK: Robust control of uncertain distributed delay systems with application to the stabilization of combustion in rocket motor chambers. Automatica, 38(3), (2002), 487-497.
 Q.C. ZHONG: Robust Control of Time-Delay Systems, Springer-Verlag, London, 2006.