Xiaoxin Liao, Pei Yu's Absolute Stability of Nonlinear Control Systems, 2nd Edition PDF

By Xiaoxin Liao, Pei Yu

ISBN-10: 1402084811

ISBN-13: 9781402084812

ISBN-10: 140208482X

ISBN-13: 9781402084829

Following the new advancements within the box of absolute balance, Prof. Xiaoxin Liao, together with Prof. Pei Yu, has created a moment variation of his seminal paintings at the topic. Liao starts with an advent to the Lurie challenge and Lurie keep an eye on method, ahead of relocating directly to the easy algebraic adequate stipulations for absolutely the balance of self sustaining and non-autonomous ODE platforms, in addition to a number of distinctive sessions of Lurie-type platforms. the point of interest of the booklet then shifts towards the hot effects and examine that experience seemed within the decade because the first version used to be released. This e-book is aimed for use by way of undergraduates within the components of utilized arithmetic, nonlinear keep watch over platforms, and chaos regulate and synchronisation, yet can also be valuable as a reference for researchers and engineers. The e-book is self-contained, notwithstanding a uncomplicated wisdom of calculus, linear method and matrix concept, and traditional differential equations is a prerequisite.

Show description

Read or Download Absolute Stability of Nonlinear Control Systems, 2nd Edition (Mathematical Modelling: Theory and Applications) PDF

Similar applied mathematicsematics books

Download PDF by George J. Huffman, Robert F. Adler, David T. Bolvin, Eric J.: Satellite Rainfall Applications for Surface Hydrology

Whereas there are increasingly more high-resolution space-based structures for measuring precipitation, circumstances of using those items for floor hydrology are infrequent. This publication, which covers either medical and sensible concerns, goals to alter that. With contributions from a panel of researchers from quite a lot of fields, the chapters specialize in comparing the capability, software and alertness of excessive solution satellite tv for pc precipitation items with regards to floor hydrology.

Read e-book online Frommer's Norway (2005) (Frommer's Complete) PDF

You will by no means fall into the vacationer traps should you trip with Frommer's. it really is like having a pal convey you round, taking you to the areas locals like most sensible. Our professional authors have already long gone far and wide you could pass — they have performed the legwork for you, and they are now not afraid to inform it love it is, saving you money and time.

Extra resources for Absolute Stability of Nonlinear Control Systems, 2nd Edition (Mathematical Modelling: Theory and Applications)

Example text

Usually one only knows that f belongs to F[0,k] , F[0,k] , or F[k1 ,k2 ) . Any other information is not available in practice. For example, for the above centrifugal governor, the control signal σ of the governor is proportional to the change of the sliding valve’s position, ∆s. f (σ ) measures the amount of the gasoline entering into the server, which is a nonlinear function of the open degree of the sliding valve. Besides knowing that when σ > 0, f (σ ) > 0 (which means a increase of the gasoline in the upper part of the server cylinder), when σ < 0, f (σ ) < 0 (implying the reduction of the gasoline in the upper part of the server cylinder), and f (0) = 0, very little is known about the function f (σ ).

X. 50 3 Sufficient Conditions of Absolute Stability: Classical Methods (1) U(x) = xT B x − 2 d Tx − cT b ≥ 0 (cT x = 0), 1. 7; 2. cT B−1 d + cT B−1 c (d T B−1 d + cTb) ≤ 0; ⎧ T −1 2 ⎨ (1) cT b + η TB−1 d − (c B d) ≤ 0, cT B−1 c where d = 12 (AT c + 2 Pb). 3. 11, we need the following lemma. 12. For any symmetric matrix B, we have cT b + d TB−1 d ≥ 0, where d= 1 T (A c + 2 Pb), 2 Proof. 2) σ 0 P A + ATP = − B. f (σ ) dσ . Then we have x f (σ ) = T B −d − d T − cT b x f (σ ) . 19) Since B is positive definite, det B > 0.

M, and fii (t, xi ) xi ≤ 0, i = m + 1, 2, . . , n; 2. There exist functions Fii (xi ) on (−∞, +∞) (i = 1, 2, . . , n), which are continuous or have only finite discontinuous points of the first or third kind such that ⎧ Fii (xi ) xi > 0 f or xi = 0, i = 1, 2, . . , m, ⎪ ⎪ ⎪ ⎪ ⎨ Fii (xi ) xi ≥ 0, i = m + 1, m + 2, . . , n, ⎪ ⎪ ⎪ ⎪ ⎩ ±∞ 0 Fii (xi ) dxi |Fii (xi )| ≤ | fii (t, xi )|, 3. The matrix A(ai j (t, x))n×n + 0<ε i = 1, 2, . . , m, = +∞, i = 1, 2, . . , n; ε Im×m 0 0 0 is negative semi-definite, where n×n 1, and ⎧ −1, i = j = 1, 2, .

Download PDF sample

Absolute Stability of Nonlinear Control Systems, 2nd Edition (Mathematical Modelling: Theory and Applications) by Xiaoxin Liao, Pei Yu


by Michael
4.2

Rated 4.73 of 5 – based on 42 votes