Full Order Dynamic Output Feedback H∞ Control For Continuous-time Switched Linear Systems

This paper is devoted to the analysis and solution of the output feedback H∞ control design problem for continuous-time switched linear systems. More specifically, the main goal is to design a switching rule together with a full order dynamic linear controller to satisfy a pre-specified H ∞ level defined by the L2 gains from the input to the output signal. The results reported in this paper are based on the so called Lyapunov-Metzler inequalities which express a sufficient condition for switched linear systems global stability. The solution of the previously mentioned output feedback control design problem through an LMI-based method is the main contribution of the present paper. An academic example borrowed from the literature is used for illustration. ©2009 IEEE.63776382Branicky, M.S., Multiple Lyapunov functions and other analysis tools for switched and hybrid systems (1998) IEEE Trans. Automat. Contr., 43, pp. 475-482Deaecto, G.S., (2007) Control Sinthesis for Dynamic Switched Systems (in Portuguese), , Master's thesis, FEEC - UnicampDeCarlo, R.A., Branicky, M.S., Pettersson, S., Lennartson, B., Perspectives and results on the stability and stabilizability of hybrid systems (2000) Proceedings of the IEEE, 88, pp. 1069-1082Garg, K.M., (1998) Theory of Differentiation: A Unified Theory of Differentiation Via New Derivate Theorems and New Derivatives, , Wiley-InterscienceGeromel, J.C., Colaneri, P., Stability and stabilization of continuous-time switched linear systems (2006) SIAM J. Control Optim., 45, pp. 1915-1930Geromel, J.C., Colaneri, P., Bolzern, P., Dynamic output feedback control of switched linear systems (2008) IEEE Trans. on Automatic Contr., 53, pp. 720-733Geromel, J.C., Deaecto, G.S., Switched state feedback control for continuous-time uncertain systems (2009) Automatica, 45, pp. 593-597Geromel, J.C., Korogui, R.H., Bernussou, J., On H2 and H∞ robust output feedback control for continuous-time polytopic systems (2007) IET Control Theory and Applications, 1, pp. 1541-1549Hu, T., Ma, L., Lin, Z., On several composite quadratic Lyapunov functions for switched systems (2006) Proceedings of the 45th IEEE Conf. on Decision and Control, pp. 113-118. , San Diego, USAJi, Z., Wang, L., Xie, G., Quadratic stabilization of switched systems (2005) Inter. Jour. of Systems Science, 36, pp. 395-404Ji, Z., Guo, X., Wang, L., Xie, G., Robust H∞ control and stabilization of uncertain switched linear systems: A multiple Lyapunov function approach (2006) ASME Journal of Dynamic Systems, Measurement, and Control, 128, pp. 696-700Lasdon, L.S., (1970) Optimization Theory for Large Systems, , Macmillan, NYLiberzon, D., Morse, A.S., Basic problems in stability and design of switched systems (1999) IEEE Control Syst. Mag., 19, pp. 59-70Liberzon, D., (2003) Switching in Systems and Control, , Birkhäuser, BostonPeleties, P., DeCarlo, R.A., Asymptotic stability of m-switched systems using Lyapunov-like functions (1991) Proceedings American Control Conference, pp. 1679-1684. , Boston, MASavkin, A.V., Petersen, I.R., Skafidas, E., Evans, R.J., Hybrid dynamical systems: Robust control synthesis problems (1996) Systems & Control Letters, 29, pp. 81-90Savkin, A.V., Skafidas, E., Evans, R.J., Robust output feedback stabilizability via controller switching (1999) Automatica, 35, pp. 69-74Skafidas, E., Evans, R.J., Savkin, A.V., Petersen, I.R., Stability results for switched controller systems (1999) Automatica, 35, pp. 553-564Sun, Z., Ge, S.S., (2005) Switched Linear Systems: Control and Design, , Springer, LondonXie, G., Wang, L., Periodical stabilization of switched linear systems (2005) Journal of Computational and Applied Mathematics, 181, pp. 176-187Zhao, J., Hill, D.J., On stability L2 gain and H∞ control for switched systems (2008) Automatica, 44, pp. 1220-123