Advanced Topics in Nonlinear Control Systems by T P Leung, Hua Shu Qin

By T P Leung, Hua Shu Qin

Over the past 50 years or so, a few textbooks, monographs or even renowned books were released on nonlinear regulate conception and layout tools. within the quarter of classical keep watch over, for instance, there exist books occupied with phase-plane research, describing functionality procedure, absolute balance etc. within the sector of contemporary regulate there are these relating to optimum regulate, utilizing differential geometry and the differential algebra technique, variable structural regulate, H-infinite keep watch over etc. those books were beneficial in selling the improvement of automated keep watch over technological know-how and know-how. due to the fact that 1990 there were many new effects and contributions within the quarter of nonlinear regulate. This publication introduces these subject matters to readers. it's going to additionally profit automation engineers, researchers and students in similar fields.

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We have only to prove it under a local coordinate frame. 10) holds iff JeMJTe = M . 12) 7 M$ We consider the following example. 14) 36 D. 13). • Before end, we leave searching structure-preserving algorithm for further study. But we give some examples to show that some algorithms preserving symplectic structure (Feng et. al 1994, Wang 1994) also preserves other structures. 7 Assume the system x = XH has an invariant structure determined by N. 14) for any N. 1. 15) where s is the step length. Then it preserves any structure.

The systems discussed in Maschke et. al 1998, etc. 11) i =0 Proof. Since A is integrable, we can find at each p a local coordinate chart, (x,z), such that A-spam—,i=l,---,dim(A)\. [dxt Note that under such a canonical j coordinate chart the structure matrix M can be expressed as r M{x) = Mx(x,z) 0 M2(x,z)) 0 It is easy to prove that the assumption Al is coordinate free. It implies that M 2 (x, z) = 0 . 11) follows immediately. • The coordinate frame, (x, z), in the above proof is said to be friend to A.

N-k. 2) then the system is stabilizable. Proof.

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