System Theory

Download Analysis and Synthesis of Dynamical Systems with Time-Delays by Yuanqing Xia PDF

By Yuanqing Xia

Time-delay happens in lots of dynamical platforms reminiscent of organic platforms, chemical structures, metallurgical processing platforms, nuclear reactor, lengthy transmission strains in pneumatic, hydraulic structures and electric networks. in particular, lately, time-delay which exists in networked keep an eye on structures has introduced extra advanced challenge right into a new learn quarter. usually, it's a resource of the iteration of oscillation, instability and negative functionality. massive attempt has been utilized to diverse facets of linear time-delay structures in the course of fresh years. as the advent of the hold up issue renders the process research extra advanced, as well as the problems because of the perturbation or uncertainties, within the keep an eye on of time-delay structures, the issues of strong balance and strong stabilization are of significant importance.

This publication provides a few simple theories of balance and stabilization of platforms with time-delay, that are with regards to the most ends up in this publication. extra cognizance may be paid on synthesis of structures with time-delay. that's, sliding mode keep an eye on of platforms with time-delay, networked keep an eye on platforms with time-delay, networked information fusion with random delay.

Show description

Read or Download Analysis and Synthesis of Dynamical Systems with Time-Delays PDF

Best system theory books

Nonholonomic Mechanics and Control

This booklet is meant for graduate and complicated undergraduate scholars in arithmetic, physics and engineering who desire to examine this topic and for researchers within the quarter who are looking to improve their ideas.

Optimal control, stabilization and nonsmooth analysis

This edited publication comprises chosen papers awarded on the Louisiana convention on Mathematical keep an eye on concept (MCT'03), which introduced jointly over 35 sought after international specialists in mathematical keep an eye on conception and its purposes. The e-book kinds a well-integrated exploration of these parts of mathematical regulate idea during which nonsmooth research is having an incredible influence.

Complex Adaptive Systems: An Introduction to Computational Models of Social Life

This e-book offers the 1st transparent, entire, and available account of advanced adaptive social structures, by way of of the field's best specialists. Such systems--whether political events, inventory markets, or ant colonies--present probably the most fascinating theoretical and functional demanding situations confronting the social sciences.

Statistical Mechanics of Complex Networks (Lecture Notes in Physics)

Networks offers an invaluable version and photo photograph worthwhile for the outline of a wide number of web-like buildings within the actual and man-made realms, e. g. protein networks, nutrients webs and the web. The contributions amassed within the current quantity offer either an advent to, and an outline of, the multifaceted phenomenology of complicated networks.

Extra info for Analysis and Synthesis of Dynamical Systems with Time-Delays

Sample text

By the method provided in [201], it was reported that the maximum allowed delay is 42. 1, it is found that system is still stable when the time-delay is 55, and could be even larger. 6) where ⎡ A ⎢I ⎢ ⎢ A¯ = ⎢ ... ⎢ ⎣0 0 ⎡ T ⎤ ⎡ ⎤ Ad Ea D ⎢ 0 ⎢0⎥ 0 ⎥ ⎢ ⎥ ⎢ ⎥ .. ⎥ , D . ⎥ , E ¯ =⎢ ¯T = ⎢ ⎢ .. ⎥ ⎢ ⎥ . ⎥ ⎢ ⎢ . ⎥ ⎣ 0 ⎣0⎦ 0 ··· 0 0 ⎦ 0 ··· I 0 EdT 0 0 0 .. ··· ··· .. 0 0 .. ⎤ ⎥ ⎥ ⎥ ⎥. 6) referred in [13], the following result is given. 4. 1) with uncertainty is quadratically stable if and only if there exist a definite positive matrix P and a positive scalar satisfying the following inequality: 28 3 Stability and Stabilization for Discrete Systems with Time-Delay ⎡ ¯ T E¯ −P + E ¯ ⎣ PA 0 ⎤ A¯T P 0 ¯ ⎦ < 0.

3) where D = diag α1 (t)Ia1 ×a1 α2 (t)Ia2 ×a2 · · · αp (t)Iap ×ap Dd = diag β1 (t)Iad1 ×ad1 β2 (t)Iad2 ×ad2 · · · βq (t)Iadq ×adq . 5) SDd = {Yd |Yd = diag Yd1 Yd2 · · · Ydq 0 < Ydi = Ydi T ∈ Radi ×adi }. 1), a nonsingular matrix T can be chosen such that TB = 0(n−m)×m B2 where B2 ∈ Rm×m is nonsingular. , B = U1 U2 Σ VT 0(n−m)×m where Σ ∈ Rm×m is a diagonal positive-definite matrix and V ∈ Rm×m is a unitary matrix. 6) where A = T AT −1 , Ad = T Ad T −1 , ΔA = T ΔAT −1 , ΔAd = T ΔAd T −1 and ϕ(t) = T ϕ(t).

20) ⎢ T ¯ ⎦ ⎣ 0 λD −λI 0 ¯ EV + Eb Y I1 0 0 −λI −1 Then, the state feedback K = Y V11 will result in the closed-loop system being quadratically stable. Proof. 17) is satisfied, that is, ¯ (k)(E˜ + E)) ¯ T −Q V T (A˜ + DF T ¯ (k)(E˜ + E))V ¯ (A˜ + DF Q−V −V <0 which can be written as −Q V T A˜T ˜ AV Q − V − V T + 0 ¯ ˜ ¯ F (k) (E + E)V 0 D 0 ¯ + [ ¯ F (k) (E˜ + E)V 0 ]T < 0. 3 Main Results 33 ⎡ ⎤ ˜ + E)V ¯ ˜ + E) ¯ T (E V T A˜T 0 −Q + V (E ⎣ ¯ ⎦ < 0. ˜ AV Q − V − V T −1 D −1 ¯ T −1 D − I 0 ˜ + E) ¯ T (E˜ + E)V ¯ , it Using Schur complement with respect to the term V (E yields ⎡ ⎤ ¯ T −Q V T A˜T 0 V (E˜ + E) ⎢ ⎥ ˜ ¯ AV Q − V − V T −1 D 0 ⎢ ⎥ < 0.

Download PDF sample

Rated 4.81 of 5 – based on 31 votes