By T P Leung, Hua Shu Qin

During the last 50 years or so, a couple of textbooks, monographs or even well known books were released on nonlinear keep an eye on thought and layout tools. within the quarter of classical keep watch over, for instance, there exist books considering phase-plane research, describing functionality process, absolute balance and so forth. within the zone of contemporary keep watch over there are these regarding optimum keep watch over, utilizing differential geometry and the differential algebra approach, variable structural keep an eye on, H-infinite regulate etc. those books were priceless in selling the advance of computerized regulate technology and know-how. because 1990 there were many new effects and contributions within the zone of nonlinear keep an eye on. This e-book introduces these issues to readers. it's going to additionally gain automation engineers, researchers and students in comparable fields.

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J. E. Marsden, (1978), Foundations of Mechanics, 2nd Ed. Benjamin / Cummings Pub. Com. Inc. P. Novikov, Symplectic geometry, (1980) in Dynamical Systems IV, Encyclopedia if Mathematical Sciences, Vol. , (1986)Introduction to Differentiable Manifolds and Riemannian Geometry, 2nd ed. Academic Press, INC. [5] Brockett R. , (1977) Control theory and analytic mechanics, in Geometric Control Theory, C. Martin and R. Sci. al, (1998), On generalized Hamiltonian systems, Proc. , Z. Xi, Y. Hong, and H.

12 Stabilization and Hx control for dissipative Hamiltonian systems The following two propositions have been proved for standard Hamiltonian systems. ). Using parallel arguments, one can see that they remain true for the controlled dissipative Hamiltonian systems. 1) is passive. 42 D. 1) is stabilizable. 3 LetR bean nxn symmetric matrix, and g is an nxm matrix. Then there exists an mxm symmetric matrix P such that R + gPg1 >0 if and only if Span{R} + Span{g} = R" Proof. (Sufficiency) Choose a coordinate frame such that R= 0 0 where k = rank(R).

Choosing CC = \IE it is easy to see that aG — R>0. 8) 46 D. Cheng It is easy to see that there exists a constant a such that c = min{a,a2/2} . a2 SoaR + — Gj - G 2 >c(R + Gi)-G2 ^ 0 . 7) is satisfied. 1) again. It is easy to see that the equilibrium of the system is _ 1 . e. —— ^ (xd-xd)V}Td — <1. and it is easy to know that 0<5q

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