(c) The system is controllable but not observable. in Visual Studio .NET

Creator QR-Code in Visual Studio .NET (c) The system is controllable but not observable.

(c) The system is controllable but not observable.
Reading QR Code ISO/IEC18004 In .NET Framework
Using Barcode Control SDK for .NET framework Control to generate, create, read, scan barcode image in VS .NET applications.
QR Code ISO/IEC18004 Maker In Visual Studio .NET
Using Barcode generation for VS .NET Control to generate, create Denso QR Bar Code image in VS .NET applications.
CHAP, 71
Recognizing QR Code 2d Barcode In .NET Framework
Using Barcode decoder for VS .NET Control to read, scan read, scan image in Visual Studio .NET applications.
Painting Barcode In VS .NET
Using Barcode creation for VS .NET Control to generate, create barcode image in .NET applications.
STATE SPACE ANALYSIS
Barcode Reader In .NET Framework
Using Barcode recognizer for .NET Control to read, scan read, scan image in VS .NET applications.
QR Code Generation In C#
Using Barcode maker for .NET framework Control to generate, create QR-Code image in .NET framework applications.
Consider the network shown in Fig. 7-26. Find a state space representation for the network with the state variables q , ( t ) = i,(t), q , ( t ) = o&) and outputs y , ( t ) = i , ( t ) , y , ( t ) = uc(t), assuming R , = R , = 1 $2, L = 1 H, and C = 1 F.
Create QR In .NET
Using Barcode generation for ASP.NET Control to generate, create QR Code 2d barcode image in ASP.NET applications.
QR-Code Generator In Visual Basic .NET
Using Barcode generator for VS .NET Control to generate, create QR Code image in .NET framework applications.
Fig. 7-26
Print Universal Product Code Version A In .NET Framework
Using Barcode generation for VS .NET Control to generate, create UPC-A Supplement 2 image in .NET framework applications.
Printing Bar Code In .NET
Using Barcode maker for .NET Control to generate, create bar code image in .NET applications.
Consider the continuous-time LTI system shown in Fig. 7-27.
Painting EAN / UCC - 13 In .NET Framework
Using Barcode generation for VS .NET Control to generate, create GS1 - 13 image in .NET applications.
Draw ISBN - 10 In .NET Framework
Using Barcode encoder for Visual Studio .NET Control to generate, create ISBN - 10 image in VS .NET applications.
( a ) Find the state space representation of the system with the state variables q , ( t ) and q , ( t ) as shown. ( 6 ) For what values of n will the system be asymptotically stable
ANSI/AIM Code 128 Encoder In Java
Using Barcode generator for Android Control to generate, create ANSI/AIM Code 128 image in Android applications.
Scan USS Code 39 In Visual Studio .NET
Using Barcode recognizer for VS .NET Control to read, scan read, scan image in .NET framework applications.
-3 (a) 4(t)=[-n
Print UPC - 13 In Java
Using Barcode generator for Eclipse BIRT Control to generate, create GS1 - 13 image in Eclipse BIRT applications.
USS-128 Generator In Java
Using Barcode encoder for BIRT reports Control to generate, create GS1 128 image in Eclipse BIRT applications.
1 l]q(t)+[y]x(t)
Barcode Encoder In Java
Using Barcode generation for Eclipse BIRT Control to generate, create bar code image in BIRT applications.
Creating Barcode In None
Using Barcode printer for Microsoft Word Control to generate, create bar code image in Office Word applications.
Fig. 7-27
Encoding Barcode In Java
Using Barcode printer for Eclipse BIRT Control to generate, create bar code image in BIRT reports applications.
Barcode Generation In Objective-C
Using Barcode creator for iPhone Control to generate, create barcode image in iPhone applications.
STATE SPACE ANALYSIS
[CHAP. 7
7 6 . A continuous-time LTI system is described by .7
s3 + 3sZ- s - 2 Write the two canonical forms of state representation for the system. H(s)= 3s2 - 1
7 6 . Consider the continuous-time LTI system shown in Fig. 7-28. .8
( a ) Find the state space representation of the system with the state variables q , ( t ) and q 2 ( t ) as shown. ( b ) Is the system asymptotically stable ( c ) Find the system function Hts). ( d l Is the system BIBO stable
y(t) =[I llq(t) The system is not asymptotically stable.
The system is BIBO stable.
F g 7-28 i.
7 6 . Find e A' for .9
( a ) Using the Cayley-Hamilton theorem method.
CHAP. 71
STATE SPACE ANALYSIS
(b) Using the spectral decomposition method.
Am, eA' =e-'
cos t -sin t
sin t cos t
Consider the matrix A in Prob. 7.69. Find e-A' and show that eWA' [eA']=
e-At=e
sin t
cos t
Find eA' for
(a) Using the diagonalization method. (b) Using the Laplace transform method.
Consider the network in Prob. 7.65 (Fig. 7.26). Find u,(t) if x(t) = u(t) under an initially relaxed condition.
v,(t)= $0 +e-'sint -e-'cost),
Using the state space method, solve the linear differentia! equation
yV(t)
+ 3y1(t) + 2 y ( t ) = 0
with the initial conditions y(O) = 0, yl(0) = 1.
Am. y(t) = e-' - e-", t
As in the discrete-time case, controllability and observability of a continuous-time LTI system may be investigated by diagonalizing the system matrix A. A system with state space representation
where A is a diagonal matrix, is controllable if the vector b has no zero elements and is observable if the vector C has no zero elements. Consider the continuous-time system in Prob. 7.50. (a) Find a new state space representation of the system by diagonalizing the system matrix A. (b) Is the system controllable (c) IS the system observable
(a) ir(t)=
[ -A
;]*(I)
+ [;]x(t)
y(t) = [2 - llv(t) (b) The system is not controllable. ( c ) The system is observable.
Appendix A
Review of Matrix Theory
MATRIX NOTATION AND OPERATIONS
An m X n matrix A is a rectangular array of elements having m rows and n columns and is denoted as
A. Definitions:
When m = n, A is called a square matrix of order n. 2. A 1 x n matrix is called an n-dimensional row vector:
An m x 1 matrix is called an m-dimensional column uector:
3. A zero matrix 0 is a matrix having all its elements zero. 4. A diagonal matrix D is a square matrix in which all elements not on the main diagonal are zero:
Sometimes the diagonal matrix D in Eq. ( A . 4 ) is expressed as D = diag(d, d 2
APP. A]
REVIEW OF MATRIX THEORY
5. The idenrity (or unit) matrix I is a diagonal matrix with all of its diagonal elements equal to 1.
B. Operations: Let A = [ a i j l m x n , = [biilmxn, C = [C~~I,,,. B and
a. Equality of Two Matrices: A = B = , a .I J = b .11. . b. Addition:
C = A + B =s c i j = a i j + bij
c. Multiplication by a Scalar:
B = a A =s bij = a a i j
If a = - 1, then B = - A is called the negative of A.
EXAMPLE A.l
Then
Notes:
4. 5. 6.
REVIEW OF MATRIX THEORY
[APP. A
Multiplication:
B = [bijInxp, and C = [cijImxp.
Let A = [a,,],.,,
C=AB
=Cij=
aikbkj
The matrix product AB is defined only when the number of columns of A is equal to the number of rows of B. In this case A and B are said to be conformable.
EXAMPLE A.2
Then 0(1)+(-1)3 1(1) + 2(3) 2(1) + ( -3)3 but BA is not defined. 0(2)+(-I)(-1) 2(2)
+ ( -3)(
- 1)
Furthermore, even if both AB and BA are defined, in general
AB # BA
EXAMPLE A.3
Then
B=[;
.A=[:
-;] [
-:I=[-: -:I=[-:
0 31
-:]2 0
A n example of the case where AB = BA follows.
EXAMPLE A.4
Let 1
~ = [ o 41
Then
AB=BA=[~
Notes: 1. AO=OA=O 2. A1 = LA = A 3. (A + B)C = AC + BC 4. A ( B + C ) = A B + A C 5. (AB)C = A(BC) = ABC 6. a(AB) = (aA)B = A(aB)
APP. A]
Copyright © OnBarcode.com . All rights reserved.