New PDF release: Absolute Stability of Nonlinear Control Systems

By Xiao-Xin Liao

ISBN-10: 9401706085

ISBN-13: 9789401706087

ISBN-10: 9401706107

ISBN-13: 9789401706100

This quantity offers an summary of a few contemporary advancements on absolutely the balance of nonlinear keep watch over systems.
bankruptcy 1 introduces the most instruments and the critical effects utilized in this e-book, resembling Lyapunov features, K-class features, Dini-derivatives, M-matrices and the relevant theorems on international balance. bankruptcy 2 offers absolutely the balance conception of independent regulate platforms and the well known Lurie challenge. bankruptcy three provides a few uncomplicated algebraic worthwhile and enough stipulations for absolutely the balance of a number of unique keep watch over structures. bankruptcy four discusses nonautonomous and discrete keep watch over platforms. bankruptcy five offers with absolutely the balance of keep watch over structures with m nonlinear keep an eye on phrases. bankruptcy 6 devotes itself to absolutely the balance of keep an eye on platforms defined by way of sensible differential equations.
The ebook concludes with an invaluable bibliography.
For utilized mathematicians, and engineers whose paintings comprises regulate systems.

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Extra resources for Absolute Stability of Nonlinear Control Systems

Sample text

Dy dt = (B + Oox

Assume tllat there exist ri>O (i= 1 ••••• ,,) sueh tllat - rlJjJ > ~ri/bii/' ;-1 i = 1 ... b. ~~ri/b.... /. b. > ~ri/b.... h. h. ~ ~rdh;/. 4. 10) is absolutely slable• Prool.

Choosing where P satisfies . ATP+PA=- B, 2. Il = <2. 9) is positive definite for x ,/«(1) ,which is impos- sible. Hence, we conclude that cTb Theorem 2. 4. 6. + 1JTB- I 1J ~ O. " , Proo/. (ii) eTB-I~O. We will complete the proof by proving ( 1 )=>( 1 )=>( 1 )=>( 1 ). , - m B - I TB 1 e, e c > Ofor eTXo > o. m being a constant, Choosing 51 2. 4. Direct Control S",tema u(x)= xTBX - 27JTx - eTb = [7JT(B-I)T _ eTB-I7J_- meT(B-I)TJB[B-I7J _ eTB- I7J - mB-IeJ eTB le eTB le _ 27JT[B-I7J - eTB- I7J - mB-leJ- eTb.

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Absolute Stability of Nonlinear Control Systems by Xiao-Xin Liao

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