This paper introduces the concept of consistency for continuous-time switched linear systems having the switching function as a primary control signal to be designed. 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 the 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. Moreover, with this property it is not necessary to assume that all the subsystems are not stabilizable in order to make a switching strategy design problem well posed. The theory is illustrated by means of several academic examples. © 2011 IFAC.18PART 158495854Boyd, S.P., El Ghaoui, L., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities in System and Control Theory, , SIAM, PhiladelphiaColaneri, P., Geromel, J.C., Astolfi, A., Stabilization of continuous-time switched nonlinear systems (2008) Systems & Contr. Letters, 57, pp. 95-103Deaecto, G.S., Geromel, J.C., H ∞ control for continuous-time switched linear systems (2010) ASME Jour. of Dynamic Syst., Measur., and Control, 132. , number 041013Decarlo, 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 continuous-time switched linear systems (2006) SIAM J. Control Optim., 45, pp. 1915-1930Geromel, J.C., Deaecto, G.S., Multi-objective H 2 control via switched linear systems (2007) Proc. of the 3rd IFAC Symposium on System, Structure and ControlGeromel, J.C., Deaecto, G.S., Switched state feedback control for continuous-time uncertain systems (2009) Automatica, 45, pp. 593-597Geromel, J.C., Colaneri, P., Bolzern, P., Dynamic output feedback control of switched linear systems (2008) IEEE Trans. on Automat. Contr., 53, pp. 720-733Hespanha, J.P., Morse, A.S., Switching between stabilizing controllers (2002) Automatica, 38, pp. 1905-1917Ji, 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., Guo, X., Wang, L., Xie, G., Robust H ∞ control and stabilization of uncertain switched linear systems: A multiple Lyapunov function approach (2006) ASME Jour. of Dynamic Syst., Measur., and Control, 128, pp. 696-700Liberzon, D., (2003) Switching in Systems and Control, , BirkhauserLiberzon, D., Morse, A.S., Basic problems in stability and design of switched systems (1999) IEEE Contr. Systems Magazine, 19, pp. 59-70Lin, H., Antsaklis, P.J., Stability and stabilizability of switched linear systems: A survey of recent results (2009) IEEE Trans. Automat. Contr., 54, pp. 308-322Savkin, A.V., Petersen, I.R., Skafidas, E., Evans, R.J., Hybrid dynamical systems: Robust control synthesis problems (1996) Systems & Contr. Letters, 29, pp. 81-90Der Van Schaft, A.J., Schumacher, J.M., (2000) An Introduction to Hybrid Dynamical Systems, , SpringerShorten, 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, , SpringerYan, P., Ozbay, H., On switching H ∞ controllers for a class of linear parameter varying systems (2007) Systems & Contr. Letters, 56, pp. 504-511Zhai, G., Hu, B., Yasuda, K., Michel, A.N., Disturbance attenuation properties of time-controlled switched systems (2001) Jour. of the Franklin Institute, 338, pp. 765-779Zhai, G., Lin, H., Kim, Y., Imae, J., Kobayashi, T., L 2 gain analysis for switched systems with continuous-time and discrete-time subsystems (2005) Int. Jour. of Contr., 78, pp. 1198-1205Zhao, J., Hill, D.J., On stability L 2 gain and H∞ control for switched systems (2008) Automatica, 44, pp. 1220-1232