Download Absolute Stability of Nonlinear Control Systems by Xiao-Xin Liao PDF

By Xiao-Xin Liao

This quantity offers an outline of a few fresh advancements on absolutely the balance of nonlinear regulate systems.
bankruptcy 1 introduces the most instruments and the valuable effects utilized in this publication, reminiscent of Lyapunov capabilities, K-class features, Dini-derivatives, M-matrices and the vital theorems on international balance. bankruptcy 2 provides absolutely the balance concept of self sufficient keep watch over structures and the well known Lurie challenge. bankruptcy three provides a few easy algebraic priceless and enough stipulations for absolutely the balance of a number of unique keep an eye on structures. bankruptcy four discusses nonautonomous and discrete keep watch over platforms. bankruptcy five bargains with absolutely the balance of keep an eye on platforms with m nonlinear keep an eye on phrases. bankruptcy 6 devotes itself to absolutely the balance of regulate platforms defined through practical differential equations.
The ebook concludes with an invaluable bibliography.
For utilized mathematicians, and engineers whose paintings comprises keep watch over systems.

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XI) ~F;j(x)/;j(Xj) j-l is negative definite with respect to y. (e;) e + ~efl;(e;) + < o. Since is arbitrary, we can find that dV! . h respect to y. ) Hence, the proof is finished. 2. m. (x)/;;(x;)x;~O. •. Cj IFiJ(x)/jj(Xj) " I + ~c; IF1,(x)/;j(Xj) I < cjIFjj(x)/jj(Xj) . I+ ;-1 1,,"' ~cdF;j(x)//j(x) ;=1 iiLj O for Xj =1= ,n) such that o. m • I ~ o. n. 23 1. 10. lll8 with Sepanble Variablee then the zero sollllion 01 O. 9. 2) is globally stable with respect to y. Prool. 6. 10. Nonautonomous Systems witb Separable Varlables Consider the nonautonomoU8 system with separable variables r { dy • .

2. 10 is neither a Lurie direct control system, nor a Lurie indirect control system, but a more complicated critical case. Therefore, the Liapunov matrix equation AP+ATP=-G has no solution P of symmetric positive de,finite matrix for any positive definite matrix G. Thus, the traditional Lurie method, i. e. , the method of using the Lurie function (P being positive definite) 38 2. AUTONOMOUS CONTROL SYSTEMS which makes ddV t I negative definite. cannot be applied. 7. (i) Let I(XI - x,) = Xl - X,.

10. 5) + f (XI - xz), f E F, and the coefficient matrix A = ( 1) O has a pair of purely - 1 O imaginary eigenvalues. Thus, Example 2. 2. 10 is neither a Lurie direct control system, nor a Lurie indirect control system, but a more complicated critical case. Therefore, the Liapunov matrix equation AP+ATP=-G has no solution P of symmetric positive de,finite matrix for any positive definite matrix G. Thus, the traditional Lurie method, i. e. , the method of using the Lurie function (P being positive definite) 38 2.

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