References
- Bergen , R and Franks , RL . 1971 . Justification of the Describing Function method . SIAM Journal on Control , 9 : 568 – 589 .
- Bolzern, P., Colaneri, P., and Geromel J.C. (2007), ‘Optimal Switching of 1-dof Oscillating Systems’, in Hybrid Systems: Computation and Control, eds. A. Bemporad, A. Bicchi, and G.C. Buttazzo, Berlin: Springer, pp. 118–130.
- Cahen , G . 1952 . Perturbations des Oscillateurs Filters . Comptes Rendus de l'Academie des Sciences , 235 : 1614 – 1617 .
- De Koning , WL . 2003 . Digital Optimal Reduced-Order Control of Pulse-Width-Modulated Switched Linear Systems . Automatica , 39 : 1997 – 2003 .
- Gelb , A and Van der Velde , WE . 1968 . Multiple-input Describing Functions and Non-linear System Design , New York : McGraw-Hill .
- Geromel , JC and Colaneri , P . 2006 . Stability and Stablization of Continuous-time Switched Linear System . SIAM Journal on Control and Optimization , 45 : 1915 – 1930 .
- Hiskens, A. (2001), ‘Stability of Limit Cycles in Hybrid Systems’, in Proceedings 34th Hawaii International Conference on System Science, Maui, HI, pp. 1–6.
- Kalman, R.E. (1963), ‘Lyapunov Functions for the Problem of Lur’e in Automatic Control’, Proceedings of the National Academy of Science, 49, 201–205.
- Kudrewicz, J. (1969), ‘Theorems on the Existence of Periodic Vibrations Based upon the Describing Function Method’, in Proceedings of the International Federation of Automatic Control, Warsaw, Poland.
- Liberzon , D . 2003 . Switching in System and Control , Boston , , MA : Birkhäuser .
- Liberzon , D and Morse , AS . 1999 . Basic Problems in Stability and Design of Switched Systems . IEEE Control Systems Magazine , 19 : 59 – 70 .
- Lighthill , MJ and Mees , AI . 1973 . “ Stability of Nonlinear Feedback Systems ” . In Recent Mathematical Developments in Control , Edited by: Bell , DJ . 1 – 20 . London : Academic .
- Loeb , M . 1956 . “ Recent Advances in Nonlinear Servo Theory ” . In Frequency Responses , Edited by: Oldenburg , R . 260 – 268 . New York : Macmillan .
- Mees , I and Bergen , A . 1975 . Describing Functions Revisited . IEEE Transactions on Automatic Control , 20 : 473 – 478 .
- Morse , AS . 1997 . Control Using Logic-Based Switching , London : Springer-Verlag .
- Narendra , S and Taylor , JH . 1973 . Frequency Domain Criteria for Absolute Stability , New York : Academic .
- Power , HM and Tsoi , A . 1974 . A Note on Brokett's Variational Technique and a Conjecture in Stability Theory . IEEE Transactions on Automatic Control , 19 : 251 – 252 .
- Sanders , SR . 1992 . Justification of the Describing Function method for Periodically Switched Circuits . Proceedings of IEEE International Symposium on Circuits and Systems , 4 : 1887 – 1890 .
- Sanders , SR . 1993 . On Limit Cycles and the Describing Function Method in Periodically Switched Circuits . IEEE Transactions on Circuits and Systems Part I: Fundamental Theory and Applications , 40 : 564 – 572 .
- Shorten, R.N. (1996), ‘A Study of Hybrid Dynamical Systems with Application to Automotive Control’, Ph.D. thesis, Department of Electrical and Electronic Engineering, University College Dublin, Republic of Ireland.
- Shorten , RN and Narendra , K . 2003 . On Common Quadratic Lyapunov Functions for Pairs of Stable LTI Systems whose System Matrices are in Companion Form . IEEE Transactions on Automatic Control , 48 : 618 – 621 .
- Shorten , RN , Curran , P and Wulff , K . 2003 . On Time-Domain Multiplier Criteria for Single-Input Single-Output Systems . Proceedings of 42nd IEEE Conference on Decision and Control , 6 : 5621 – 5625 .
- Shorten , RN , Wirth , F , Mason , O , Wulff , K and King , C . 2007 . Stability Criteria for Switched and Hybrid Systems . SIAM Review , 49 : 545 – 592 .
- Sun , Z and Ge , SS . 2005 . Switched Linear Systems: Control and Design , London : Springer .