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International Journal of Control Volume 10, 1969 - Issue 2
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Original Articles

Piecewise-quadratic and piecewise-linear Lyapunov functions for discontinuous systemsFootnote†

STEIN WEISSENBERGER Department of Mechanical Engineering, University of Santa Clara, California, U.S.A.
Pages 171-180 | Received 28 Jul 1968, Published online: 16 Jan 2007

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XenofonD. Koutsoukos & PanosJ. Antsaklis. (2002) Design of stabilizing switching control laws for discrete- and continuous-time linear systems using piecewise-linear Lyapunov functions. International Journal of Control 75:12, pages 932-945.
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D. N. SHIELDS & C. STOREY. (1975) The behaviour of optimal Lyapunov functions. International Journal of Control 21:4, pages 561-573.
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Articles from other publishers (13)

Robert Shorten, Fabian Wirth, Oliver Mason, Kai Wulff & Christopher King. (2007) Stability Criteria for Switched and Hybrid Systems. SIAM Review 49:4, pages 545-592.
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L Gruyitch, P Borne, J Gentina & J RichardJ Richard. 2003. Stability Domains. Stability Domains.
Lijun Zhang, Daizhan Cheng & Jiang B. Liu. (2008) STABILIZATION OF SWITCHED LINEAR SYSTEMS. Asian Journal of Control 5:4, pages 476-483.
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D.Z. Liao & L.F. Yeung. (2003) l∞-based stability criteria and its applications on FLC systems. Fuzzy Sets and Systems 139:1, pages 35-57.
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K. Loskot, A. Polanski & R. Rudnicki. (1998) Further comments on "Vector norms as Lyapunov functions for linear systems". IEEE Transactions on Automatic Control 43:2, pages 289-291.
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A. Polanski. (1997) Lyapunov function construction by linear programming. IEEE Transactions on Automatic Control 42:7, pages 1013-1016.
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V.C. Aitken & H.M. Schwartz. (1994) On the exponential stability of discrete-time systems with applications in observer design. On the exponential stability of discrete-time systems with applications in observer design.
V.C. Aitken & H.M. Schwartz. (1994) On the exponential stability of discrete-time systems with applications in observer design. IEEE Transactions on Automatic Control 39:9, pages 1959-1962.
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H. Kiendl, J. Adamy & P. Stelzner. (1992) Vector norms as Lyapunov functions for linear systems. IEEE Transactions on Automatic Control 37:6, pages 839-842.
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V.I. Utkin. (1987) Discontinuous Control Systems: State of Art in Theory and Applications. IFAC Proceedings Volumes 20:5, pages 25-44.
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M.A.H. Dempster & G.M. Coupé. (1983) Investigation of the Stability of Satellite Large Angle Attitude Manoeuvres using Nonlinear Optimization Methods. IFAC Proceedings Volumes 16:11, pages 111-124.
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M.A.H. Dempster & G.M. Coupé. 1983. Automatic Control in Space 1982. Automatic Control in Space 1982 111 124 .
R. Longchamp. (1980) Stable feedback control of bilinear systems. IEEE Transactions on Automatic Control 25:2, pages 302-306.
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