By T P Leung, Hua Shu Qin

Over the past 50 years or so, a couple of textbooks, monographs or even well known books were released on nonlinear keep an eye on concept and layout tools. within the zone of classical keep an eye on, for instance, there exist books taken with phase-plane research, describing functionality strategy, absolute balance etc. within the quarter of recent keep an eye on there are these regarding optimum keep watch over, utilizing differential geometry and the differential algebra process, variable structural keep watch over, H-infinite keep watch over etc. those books were worthy in selling the improvement of computerized keep watch over technology and expertise. on the grounds that 1990 there were many new effects and contributions within the region of nonlinear keep an eye on. This ebook introduces these issues to readers. it may additionally gain automation engineers, researchers and students in similar fields.

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Z. , S. Spurgeon, J. F. Martin, (2000d) Normal form representation of control systems, submitted. , New York 50 D. J. , T. J. Clements, (1999) High gain tracking control for the nonlinear benchmark systems, Proc. J. van der Schaft, and R. , (1994) Dynamical systems and geometric construction of algorithms, in Computational Mathematics in China, Contemporary Mathematics, 163, Zhong-Ci Shi, Chung-Chun Yang, Eds. 1-31 [17] Guckenheimer, J. and P. , Springer-Verlag [19] J. Koszul, et. , (in Chinese) [20] Kunder.

1. Let N = H be symmetric. Thendim(Gfj) = «(w -1) / 2;Particularly, dim(SO(n,R)) = n(n -1)/2. 2. Let N = K be skew-symmetric. Then dim{Gj^) = n{n + \)l2 ;Particularly, dim(Sp(2n, R)) = n(2n +1) . The following theorem shows that for any N e Mn, GN is nontrivial. 5 For any nxn matrix N(n>l), words: GN is not discrete. In other dim(Gjy)>0. Proof. Decompose N as N =H +K where H is symmetric, HT = H , and K is skew-symmetric, KT =-K . We first assume H is singular. Then there exists a E, ^ 0 such that HE, = 0 .

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