By T P Leung, Hua Shu Qin

ISBN-10: 9810244428

ISBN-13: 9789810244422

Over the past 50 years or so, a few textbooks, monographs or even renowned books were released on nonlinear regulate concept and layout tools. within the sector of classical keep an eye on, for instance, there exist books all for phase-plane research, describing functionality strategy, absolute balance and so forth. within the quarter of recent keep watch over there are these regarding optimum regulate, utilizing differential geometry and the differential algebra approach, variable structural regulate, H-infinite keep an eye on and so forth. those books were worthy in selling the improvement of computerized keep an eye on technology and know-how. given that 1990 there were many new effects and contributions within the zone of nonlinear keep watch over. This booklet introduces these subject matters to readers. it's going to additionally profit automation engineers, researchers and students in similar fields.

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**Example text**

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). Let g = 81 . Then rank(gl) = n-k . 1) > 0, where P = QQ . (Necessary) Suppose rank(gi)

The following proposition shows that these two forms are equivalent. 4 Let a be a non-singular quadratic tensor field and {•,•} be the pseudo-Poisson bracket induced by co as in above. ") Proof. 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.

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).

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

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