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

The aim of this paper is to present new results on 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 equations arisen from H∞ theory. The proposed algorithm is simple, efficient and easy to implement. Some examples illustrating state and output feedback design are solved and discussed in order to put in evidence the most relevant characteristic of the theoretical results. Moreover, a practical application involving a 3-DOF networked control system is presented. © 2012 EUCA.185425436Boukas, E.-K., Liu, Z.-K., (2002) Deterministic and Stochastic Time Delay Systems, Control Engineering, , Birkhäuser, BostonByrd, R.H., Schnabel, R.B., Continuity of the null space basis and constrained optimization (1986) Math Program, 35 (1), pp. 32-41Choi, H.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 RH2-RH∞ Viewpoint, , Academic Press Inc., London, UKde Oliveira, M.C., Geromel, J.C., Synthesis of non-rational controllers for linear delay systems (2004) Automatica, 40 (2), pp. 171-188de Oliveira, M.C., Souza, F.O., Palhares, R.M., Assessing Stability of Time-Delay Systems Using Rational Systems (2008) Proceedings of the 47th IEEE Conference on Decision and Control, pp. 4012-4017. , Cancun, Mexico, December 9-11Fridman, E., Shaked, U., New bounded real lemma representations for time-delay systems and their applications (2001) IEEE Trans Autom Control, 46 (12), pp. 1973-1979Fridman, E., Shaked, U., A descriptor system approach to H∞ control of linear time-delay systems (2002) IEEE Trans Autom Control, 47 (2), pp. 253-270Ge, J.-H., Frank, P.M., Lin, C.-F., H∞ control via output feedback for state delayed systems (1996) Int J Control, 64 (1), pp. 1-7Gu, K., Kharitonov, V.L., Chen, J., (2003) Stability of Time-Delay Systems, Control Engineering, , Birkhäuser, BostonHespanha, J.P., Naghshtabrizi, P., Xu, Y., A survey of recent results in networked control systems (2007) Proc 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 Signal Process, 59 (3), pp. 979-988Lee, J.H., Kim, W., Kwon, W.H., Memoryless H∞ controllers for state delayed systems (1994) IEEE Trans Autom Control, 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 Control, 47 (5), pp. 793-797(2010) 3 DOF Hover System, , www.quanser.com, QuanserRekasius, 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: Anoverviewof 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 Control, 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 J Robust Nonlinear 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 Trans Autom Control, 50 (8), pp. 1177-1181Zhang, W., Branicky, M.S., Phillips, S.M., Stability of networked control systems (2001) IEEE Control Syst Mag, pp. 84-99Zhou, K., Doyle, J.C., (1998) Essentials of Robust Control, , Prentice Hall, New Jerse