Switching Control Consistency Analysis For Discrete-time Switched Linear Systems

This paper introduces the concept of consistency for discrete-time switched linear systems having the switching function as a primary control signal to be designed, and also proposes a certification of how consistent is such switching function. A state feedback switching control strategy is strictly consistent whenever it improves performance compared to the ones of all isolated subsystems. It is proven that a min-type switching strategy is strictly consistent for classes of H 2 and H ∞ performance indexes. This property makes clear the importance of switching systems control design in both theoretical and practical application frameworks. The theory is illustrated by means of academic examples. © 2012 IFAC.7PART 1599604Danfoss,Grundfos,DONG Energy,VestasBlanchini, F., Casagrande, D., Gardonio, P., Miani, S., On optimal damping of vibrating structures (2011) 18 th IFAC World Congress, pp. 10268-10273. , Preprints of theBoyd, S.P., El Ghaoui, L., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities in System and Control Theory, , SIAM, PhiladelphiaDeaecto, G.S., Geromel, J.C., Daafouz, J., Dynamic output feedback H ∞ control of switched linear systems (2011) Automatica, 47, pp. 1713-1720De Carlo, R.A., Branicky, M.S., Pettersson, S., Lennartson, B., Perspectives and results on the stability and stabilizability of hybrid systems (2000) Proc. of the IEEE, 88, pp. 1069-1082Geromel, J.C., Colaneri, P., Stability and stabilization of discrete time switched systems (2006) Int. J. of Contr., 79, pp. 719-728Geromel, J.C., Colaneri, P., Bolzern, P., Dynamic output feedback control of switched linear systems (2008) IEEE Trans. on Automat. Contr., 53, pp. 720-733Geromel, J.C., Deaecto, G.S., Daafouz, J., Suboptimal switching state feedback control consistency analysis for switched linear systems (2011) 18 th IFAC World Congress, pp. 5849-5854. , Preprints of theJi, Z., Wang, L., Xie, G., Quadratic stabilization of uncertain discrete-time switched systems via output feedback (2005) Circuits Syst. Sign. Processing, 24, pp. 733-751Ji, Z., Wang, L., Xie, G., Quadratic stabilization of switched systems (2005) Int. J. of Syst. Science, 36, pp. 395-404Lasdon, L.S., (1970) Optimization Theory for Large Systems, , MacmillanLiberzon, D., (2003) Switching in Systems and Control, , BirkhuserLiberzon, D., Morse, A.S., Basic problems in stability and design of switched systems (1999) IEEE Contr. Syst. Magazine, 19, pp. 59-70Lin, H., Antsaklis, P.J., Switching stabilization and l 2 gain performance controller synthesis for discrete-time switched linear systems (2006) Proc. of the 45th IEEE Conf. on Dec. and Contr., pp. 2673-2678Lin, H., Antsaklis, P.J., Hybrid state feedback stabilization with ℓ 2 performance for discrete-time switched linear systems (2008) Int. Jour. of Contr., 81, pp. 1114-1124Lin, H., Antsaklis, P.J., Stability and stabilizability of switched linear systems: A survey of recent results (2009) IEEE Trans. Automat. Contr., 54, pp. 308-322Shorten, R., Wirth, F., Mason, O., Wulff, K., King, C., Stability criteria for switched and hybrid systems (2007) SIAM Rev., 49, pp. 545-592Sun, Z., Ge, S.S., (2005) Switched Linear Systems: Control and Design, , Springer, LondonZhai, G., Quadratic stabilizability of discrete-time switched systems via state and output feedback (2001) Proc. of the 40th IEEE Conf. on Dec. and Contr., pp. 2165-2166Zhai, G., Lin, H., Antsaklis, P., Quadratic stabilizability of switched linear systems with polytopic uncertainties (2003) Int. J. of Contr., pp. 747-75