On A Rational Transfer Function-based Approach To H∞ Filtering Design For Time-delay Linear Systems

This paper introduces a new procedure for H∞ filter design of time-delay linear systems. A finite-order LTI system, called comparison system, is defined in such a way that its H∞ norm is proven to be strongly related to the one of the time-delay system. Differently from what can be viewed as a common feature of filter design methods available in the literature to date, the one presented here treats the filtering design of time-delay systems with classical numerical routines based on Riccati equation and H∞ theory of LTI systems. The proposed algorithm is simple, efficient and easy to implement. Illustrative examples are solved and discussed in order to put in evidence the most relevant properties of the theoretical results. Furthermore, a practical application is presented. © 2010 IEEE.593979988Gu, K., Kharitonov, V.L., Chen, J., (2003) Stability of Time-Delay Systems, Ser. Control Engineering Series, , Boston, MA: BirkhäuserNiculescu, S.I., Gu, K., (2004) Advances in Time-Delay Systems, , New York: SpringerRichard, J.-P., Time delay systems: An overview of some recent advances and open problems (2003) Automatica, 39 (10), pp. 1667-1694. , OctFridman, E., Shaked, U., A new H∞ filter design for linear time delay systems (2001) IEEE Transactions on Signal Processing, 49 (11), pp. 2839-2843. , DOI 10.1109/78.960431, PII S1053587X01092157Fridman, E., Shaked, U., An improved delay-dependent H∞ filtering of linear neutral systems (2004) IEEE Trans. Signal Process., 52, pp. 668-673. , MarZhang, X.M., Han, Q.L., Robust H∞ filtering for a class of uncertain linear systems with time-varying delay (2008) Automatica, (44), pp. 157-166Peng, C., Yue, D., Tian, E., Zhang, Y., Improved network-based robust H∞ filtering for uncertain linear systems (2009) Int. J. Innovat. Comput., Inf. Contr., 5 (4), pp. 961-970. , AprDe Oliveira, M.C., Geromel, J.C., Synthesis of nonrational controllers for linear delay systems (2004) Automatica, 40 (2), pp. 171-188. , FebGao, Z., Ding, S.X., State and disturbance estimator for time-delay systems with application to fault estimation and signal compensation (2007) IEEE Transactions on Signal Processing, 55 (12), pp. 5541-5551. , DOI 10.1109/TSP.2007.900154Li, H., Fu, M., A linear matrix inequality approach to robust H∞ filtering IEEE Trans. Autom. Control, , unpublishedOlgac, N., Sipahi, R., An exact method for the stability analysis of time-delayed linear time-invariant (LTI) systems (2002) IEEE Transactions on Automatic Control, 47 (5), pp. 793-797. , DOI 10.1109/TAC.2002.1000275, PII S001892860204761XChen, J., Gu, G., Nett, C.N., A new method for computing delay margins for stability of linear delay systems (1995) Syst. Contr. Lett., 26 (2), pp. 107-117. , SepRekasius, Z.V., A stability test for systems with delays (1980) Proc. Joint Autom. Contr. Conf., , Paper No. TP9-ATsypkin, Y.Z., Fu, M., Robust stability of time-delay systems with an uncertain time-delay constant (1993) Int. J. Control, 57 (4), pp. 865-879. , AprYoucef-Toumi, K., Bobbett, J., Stability of uncertain linear systems with time delay (1991) J. Dyn. Syst., Measure. Contr.-Trans. ASME, 113 (4), pp. 558-567. , DecKamen, E.W., Linear systems with commensurate time delays: Stability and stabilization independent of delay (1982) IEEE Trans. Autom. Control, 27 (1), pp. 367-375. , JanWalton, K., Marshall, J.E., Direct method for TDS stability analysis (1987) IEE Proceedings D: Control Theory and Applications, 134 (2), pp. 101-107Zhang, J., Knospe, C.R., Tsiotras, P., Newresults for the analysis of linear systems with time-invariant delays (2003) Int. J. Rob. Nonlin. Contr., 13 (12), pp. 1149-1175. , OctBrockett Roger, W., Byrnes Christopher, I., Multivariable Nyquist criteria, root loci, and pole placement: Ageometric viewpoint (1981) IEEE Transactions on Automatic Control, AC-26 (1), pp. 271-284Korogui, R.H., Fioravanti, A.R., Geromel, J.C., On a rational transfer function-based approach to H∞ filter design for time-delay systems (2009) Proc. 48th IEEE Conf. on Dec. Contr., pp. 1854-1859. , Shanghai, China, DecFridman, E., Shaked, U., A descriptor system approach to H∞ control of linear time-delay systems (2002) IEEE Transactions on Automatic Control, 47 (2), pp. 253-270. , DOI 10.1109/9.983353, PII S0018928602020640Niculescu, S.I., H∞ memoryless control with an α-stability constraint for time-delay systems: An LMI approach (1998) IEEE Trans. Autom. Control, 43 (5), pp. 739-743. , MayColaneri, P., Geromel, J.C., Locatelli, A., (1997) Control Theory and Design: An RH2 - RH∞ Viewpoint, , London, U.K.: AcademicZhou, K., Doyle, J.C., (1998) Essentials of Robust Control, , Englewood Cliffs, NJ: Prentice-HallGeromel, J.C., Optimal linear filtering under parameter uncertainty (1999) IEEE Trans. Signal Process., 47, pp. 168-175. , JanGeromel, J.C., Filho, L.A.V.R., H2 optimal robust filtering (2005) Eur. J. Control, 12 (1), pp. 30-39. , De