H ∞ Control Design For Time-delay Linear Systems: A Rational Transfer Function Based Approach

The aim of this paper is to cope with the H ∞ control synthesis for time-delay linear systems. We extend the use of a finite order LTI system, called comparison system to H ∞ analysis and design. Differently from what can be viewed as a common feature of other control design methods available in the literature to date, the one presented here treats time-delay systems control design with classical numeric routines based on Riccati equation and H ∞ theory. An illustrative example and a practical application involving a 3-DOF networked control system are presented. © 2011 IEEE.18661871Boukas, E.-K., Liu, Z.-K., (2002) Deterministic and Stochastic Time Delay Systems, , Control Engineering. BirkhäuserByrd, R.H., Schnabel, R.B., Continuity of the null space basis and constrained optimization (1986) Mathematical Programming, 35 (1), pp. 32-41Ho Choi, H., Chungs, M.J., Observer-based H ∞ controller design for state delayed linear systems (1995) Automatica, 32 (7), pp. 1073-1075Colaneri, P., Geromel, J.C., Locatelli, A., (1997) Control Theory and Design: An RH 2 - RH ∞ Viewpoint, , Academic Press, LondonDe Oliveira, M.C., Geromel, J.C., Synthesis of non-ratinal controllers for linear delay systems (2004) Automatica, 40 (2), pp. 171-188Fridman, E., Shaked, U., New bounded real lemma representations for time-delay systems and their applications (2001) IEEE Trans. Autom. Contr., 46 (12), pp. 1973-1979Fridman, E., Shaked, U., A descriptor system approach to H ∞ control of linear time-delay systems (2002) IEEE Trans. Autom. Contr., 47 (2), pp. 253-270Ge, J.-H., Frank, P.M., Lin, C.-F., H ∞ control via output feedback for state delayed systems (1996) Int. Jour. Contr., 64 (1), pp. 1-7Gu, K., Kharitonov, V.L., Chen, J., (2003) Stability of Time-delay Systems, , Control Eng. Series. BirkhuserHespanha, J.P., Naghshtabrizi, P., Xu, Y., A survey of recent results in networked control systems (2007) Proceedings of the IEEE, 95 (1), pp. 138-162Korogui, R.H., Fioravanti, A.R., Geromel, J.C., On a rational transfer function-based approach to H ∞ filter design for time-delay linear systems (2011) IEEE Trans. Sign. Process, 59 (3), pp. 979-988Lee, J.H., Kim, W., Kwon, W.H., Memoryless H ∞ controllers for state delayed systems (1994) IEEE Trans. Autom. Contr., 39 (1), pp. 159-162Niculescu, 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. 739-748Niculescu, S.I., Gu, K., (2004) Advances in Time-delay Systems, , SpringerOlgac, N., Sipahi, R., An exact method for the stability analysis of time-delayed linear time-invariant (lti) systems (2002) IEEE Trans. Autom. Contr., 47 (5), pp. 793-797(2010) 3 DOF Hover System, , www.quanser.comRekasius, Z.V., A stability test for systems with delays (1980) Proc. of Joint Automatic Control Conference, Paper No. TP9-ARichard, J.-P., Time delay systems: An overview of some recent advances and open problems (2003) Automatica, 39 (10), pp. 1667-1694Roesch, O., Roth, H., Niculescu, S.-I., Remote control of mechatronic systems over communication networks (2005) Proc. IEEE Inter. Conf. Mechatronics & Automation, pp. 1648-1653. , Niagara Falls, Canada, JulyShen, J.-C., Chen, B.-S., Kung, F.-C., Memoryless stabilization of uncertain dynamic delay systems: Riccati equation approach (1991) IEEE Trans. Autom. Contr., 36 (5), pp. 638-640Sipahi, R., Olgac, N., A comparison of methods solving the imaginary characteristic roots of lti time delayed systems (2005) Proceedings of the IFAC World Congress, , Prague, Czech RepublicZhang, J., Knospe, C.R., Tsiotras, P., New results for the analysis of linear systems with time-invariant delays (2003) Int. Journal Rob. Nonlin. Control, 13 (12), pp. 1149-1175Zhang, L., Shi, Y., Chen, T., Huang, B., A new method for stabilization of networked control systems with random delays (2005) IEEE Transactions on Automatic Control, 50 (8), pp. 1177-1181Zhang, W., Branicky, M.S., Phillips, S.M., Stability of networked control systems (2001) IEEE Control Systems Magazine, pp. 84-99Zhou, K., Doyle, J.C., (1998) Essentials of Robust Control, , Prentice Hall, New Jerse