You are here

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

By Xiaoxin Liao, Pei Yu

ISBN-10: 1402084811

ISBN-13: 9781402084812

ISBN-10: 140208482X

ISBN-13: 9781402084829

Following the hot advancements within the box of absolute balance, Prof. Xiaoxin Liao, along 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 process, prior to relocating directly to the straightforward algebraic adequate stipulations for absolutely the balance of independent and non-autonomous ODE platforms, in addition to numerous particular periods of Lurie-type structures. the point of interest of the ebook then shifts towards the recent effects and learn that experience seemed within the decade because the first version was once released. This ebook is aimed for use by way of undergraduates within the parts of utilized arithmetic, nonlinear keep watch over platforms, and chaos keep an eye on and synchronisation, yet can also be beneficial as a reference for researchers and engineers. The ebook is self-contained, although a simple wisdom of calculus, linear method and matrix idea, 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

Frommer's The Carolinas and Georgia (2009 9th Edition) by Darwin Porter, Danforth Prince PDF

Now with up-to-date and multiplied cultural details, Frommer's The Carolinas and Georgia ninth variation is an unbeatable consultant to a couple of the South's hottest areas to go to, remain, and play. Our advisor levels from renowned parks (Great Smoky Mountain) and terrific shorelines (the Outer Banks) to old towns (Charleston) and must-see significant metropolises (Atlanta).

Download e-book for iPad: Web Technologies: Concepts, Methodologies, Tools, and by Arthur Tatnall

With the technological development of cellular units, social networking, and digital companies, internet applied sciences maintains to play an ever-growing a part of the worldwide lifestyle, included into cultural, cost effective, and organizational degrees. internet applied sciences: techniques, Methodologies, instruments, and functions offers a finished depiction of present and destiny developments in help of the evolution of net details structures, internet purposes, and the net.

Laura Lea Miller's Frommer's Walt Disney World & Orlando 2006 (Frommer's PDF

Thoroughly up-to-date for 2006, Frommer's Walt Disney international & Orlando is the best trip-planner for America's #1 holiday destination--Disney international. In 2004, the entire Disney parks observed raises in attendance of five to nine percentage over the former 12 months. a complete of 15. 1 million humans visited the Magic country in 2004, in accordance with entertainment enterprise journal.

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

Sample text

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. Then, det B−1 0 = det B−1 = (det B)−1 > 0, 0T 1 and det B−1 0 0T 1 B −d − d T − cT b Thus, det = det I − B−1 d = − cT b − d TB−1 d. − d T − cT b B −d = (− cT b − d TB−1 d) det B. 20) is an important formula and has many applications. t. (x, f (σ )), which is, however, impossible as shown above.

N; 2. There exist constants ci > 0 (i = 1, 2, . . , m), c j ≥ 0 ( j = m + 1, . . , n) such that ⎧ n ⎪ ⎪ −c |a | + ci |ai j | < 0, j = 1, . . , m, ⎪ j j j ∑ ⎨ ⎪ ⎪ ⎪ ⎩ −c j |a j j | + i=1,i= j n ∑ ci |ai j | ≤ 0, j = m + 1, . . t. the partial variable y. Proof. We construct the Lyapunov function n V (x) = ∑ ci |xi |. t. y. 34. 38. 20) satisfies the following conditions: 1. fi (xi ) xi > 0 for xi = 0, aii < 0, i = 1, 2, . . , n, and fi (xi ) xi ≥ 0, i = m + 1, . . , n; 2. ⎡ a21 an1 ⎤ 1 − ··· − ⎢ a11 a11 ⎥ ⎢ a an2 ⎥ 21 ⎥ ⎢ 1 ··· − ⎥ ⎢ − ˜ ˜ a a ⎥ := A11 A12 , ⎢ ˜ 22 22 A := ⎢ ⎥ ˜ 21 A˜ 22 .

The partial variable y. Proof. 26 to complete the proof. 33. 18) satisfies 1. 31; 2. There exist n functions ci > 0 (i = 1, 2, . . , m) and c j ≥ 0 ( j = m + 1, . . , n) such that ⎧ n ⎪ ⎪ −c j | f j j (x j )| + ∑ ci | f j j (x j )| < 0 for x j = 0, j = 1, . . , m, ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ −c j | f j j (x j )| + i=1,i= j n ∑ ci | f j j (x j )| ≤ 0, j = m+1, . . t. the partial variable y. Proof. We construct the Lyapunov function n V (x) = ∑ ci |xi |. i=1 Clearly, m V (x) ≥ ∑ ci |xi | := ϕ (y) → +∞ y → +∞, as i=1 and ϕ (y) is positive definite.

Download PDF sample

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


by Joseph
4.0

Rated 4.59 of 5 – based on 27 votes
Top