The paper presents two different approaches, which enable a state transformation for system equations of switched linear systems to controllability canonical forms. The approaches are based on a constructive basis selection procedure for the controllability subspace and a controllability Kalman-type rank condition of switched linear systems. The results contribute to clarify the switched system structure to a certain degree under complete controllability.
Baglietto, M., Battistelli, G. and Scardovi, L.2007: Active mode observability of switching linear systems . Automatica43, 1442-49.
2.
Bemporad, A., Ferrari-Trecate, G. and Morari, M.2000: Observability and controllability of piecewise affine and hybrid systems. IEEE Transactions on Automatic Control45, 1864-76.
3.
Bemporad, A. and Morari, M.1999: Control of systems integrating logic, dynamics, and constraints . Automatica35, 407-27.
4.
Blanchini, F., Miani, S. and Savorgnan, C.2007: Stability results for linear parameter varying and switching systems. Automatica43, 1817-23.
5.
Branicky, M.S.1998: Multiple Lyapunov functions and other analysis tools for switched hybrid systems. IEEE Transactions on Automatic Control43, 475-82.
6.
Chatterjee, D. and Liberzon, D.2006: Stability analysis of deterministic and stochastic switched systems via a comparison principle and multiple Lyapunov functions. SIAM Journal on Control and Optimization45, 174-206.
7.
Cheng, D., Lin, Y. and Wang, Y.2006: Accessibility of switched linear systems,. IEEE Transactions on Automatic Control51, 1486-91.
8.
Dorissen, H.T.1989: Canonical forms for bilinear systems. Systems Control Letters13, 153-60.
9.
Ge, S.S., Sun, Z. and Lee, T.H.2001: Reachability and controllability of switched linear discrete-time systems. IEEE Transactions on Automatic Control46, 1437-41.
10.
Hickin, J. and Sinha, N.K.1979: On the transformation of linear multivariable systems to canonical forms. International Journal of Systems Science10, 783-96.
11.
Ji, Z., Feng, G. and Guo, X.2007a: A constructive approach to reachability realization of discrete-time switched linear systems. Systems Control Letters56, 669-77.
12.
Ji, Z., Guo, X. and Wang, L.2007b: Stabilization of switched linear systems with time-varying delay in switching occurrence detection. Circuits, Systems and Signal Processing26, 361-77.
13.
Ji, Z., Wang, L. and Guo, X.2007c: Design of switching sequences for controllability realization of switched linear systems. Automatica43, 662-68.
14.
Lin, H. and Antsaklis, P.J.2007: Switching stabilizability for continuous-time uncertain switched linear systems. IEEE Transactions on Automatic Control52, 633-46.
15.
Luenberger, D.G.1967: Canonical forms for linear multivariable systems. IEEE Transactions on Automatic Control12, 290-93.
16.
Sun, Y., Wang, L. and Xie, G.2006a: Delay-dependent robust stability and stabilization for discrete-time switched systems with mode-dependent time-varying delays. Applied Mathematics and Computation180, 428-35.
17.
Sun, Y., Wang, L., Xie, G. and Yu, M.2006b: Improved overshoot estimation in pole placements and its application in observer-based stabilization for switched systems. IEEE Transactions on Automatic Control51, 1962-66.
18.
Sun, Z.2004: Canonical forms of switched linear control systems. Proceedings of the 2004 American Control Conference, Boston, MA, 5182-87.
19.
Sun, Z. and Ge, S.S.2003: Dynamic output feedback stabilization of a class of switched linear systems. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications50, 1111-15.
20.
Sun, Z. and Ge, S.S.2005: Switched stabilization of higher-order switched linear systems. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005, Seville.
21.
Sun, Z., Ge, S.S. and Lee, T.H.2002: Reachability and controllability criteria for switched linear systems. Automatica38, 775-86.
22.
Xie, G. and Wang, L.2003: Controllability and stabilizability of switched linear-systems . Systems Control Letters48, 135-55.
23.
Xie, G. and Wang, L.2004: Necessary and sufficient conditions for controllability and observability of switched impulsive control systems. IEEE Transactions on Automatic Control49, 960-66.
24.
Xu, X. and Antsaklis, P.J.2004: Optimal control of switched systems based on parameterization of the switching instants. IEEE Transactions on Automatic Control49, 2-16.