Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
5th Edition
ISBN: 9780321816252
Author: C. Henry Edwards, David E. Penney, David Calvis
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 6.3, Problem 27P
Program Plan Intro
Show the linearization and eigenvalues of the non-linear system at the given critical point and construct phase plane portrait.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Apply the Network flow maximization algorithm in the text book to the network below one step at a time. At each step, show diagrams of the flow graph Gf and the residual graph Gr to each diagram to describe how you obtained it from the previous diagram. In particular, describe the policy used to select an augmenting path from s to t for adding to the flow graph when multiple options were available. What is the termination condition for your algorithm? Prove that your solution is correct
A system is said to be completely observable if there exists an unconstrained control u(t) that
can transfer any initial state x(to) to any other desired location x(t) in a finite
time to T.
b. Investigate the observability of the system below.
(X1
X2,
-2
(X1
y = [1 2]
Knowing that X = Ax + Bu and y= Cx.
4. Discuss the relation of location of poles on stability of a
system. Explain with neat graphs.
5. For a unit feedback system, G(s) = . Develop the Root
Locus. Show all the required calculations.
Chapter 6 Solutions
Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
Ch. 6.1 - Prob. 1PCh. 6.1 - Prob. 2PCh. 6.1 - Prob. 3PCh. 6.1 - Prob. 4PCh. 6.1 - Prob. 5PCh. 6.1 - Prob. 6PCh. 6.1 - Prob. 7PCh. 6.1 - Prob. 8PCh. 6.1 - Prob. 9PCh. 6.1 - Prob. 10P
Ch. 6.1 - Prob. 11PCh. 6.1 - Prob. 12PCh. 6.1 - Prob. 13PCh. 6.1 - Prob. 14PCh. 6.1 - Prob. 15PCh. 6.1 - Prob. 16PCh. 6.1 - Prob. 17PCh. 6.1 - Prob. 18PCh. 6.1 - Prob. 19PCh. 6.1 - Prob. 20PCh. 6.1 - Prob. 21PCh. 6.1 - Prob. 22PCh. 6.1 - Prob. 23PCh. 6.1 - Prob. 24PCh. 6.1 - Prob. 25PCh. 6.1 - Prob. 26PCh. 6.1 - Prob. 27PCh. 6.1 - Prob. 28PCh. 6.1 - Prob. 29PCh. 6.1 - Prob. 30PCh. 6.2 - Prob. 1PCh. 6.2 - Prob. 2PCh. 6.2 - Prob. 3PCh. 6.2 - Prob. 4PCh. 6.2 - Prob. 5PCh. 6.2 - Prob. 6PCh. 6.2 - Prob. 7PCh. 6.2 - Prob. 8PCh. 6.2 - Prob. 9PCh. 6.2 - Prob. 10PCh. 6.2 - Prob. 11PCh. 6.2 - Prob. 12PCh. 6.2 - Prob. 13PCh. 6.2 - Prob. 14PCh. 6.2 - Prob. 15PCh. 6.2 - Prob. 16PCh. 6.2 - Prob. 17PCh. 6.2 - Prob. 18PCh. 6.2 - Prob. 19PCh. 6.2 - Prob. 20PCh. 6.2 - Prob. 21PCh. 6.2 - Prob. 22PCh. 6.2 - Prob. 23PCh. 6.2 - Prob. 24PCh. 6.2 - Prob. 25PCh. 6.2 - Prob. 26PCh. 6.2 - Prob. 27PCh. 6.2 - Prob. 28PCh. 6.2 - Prob. 29PCh. 6.2 - Prob. 30PCh. 6.2 - Prob. 31PCh. 6.2 - Prob. 32PCh. 6.2 - Prob. 33PCh. 6.2 - Prob. 34PCh. 6.2 - Prob. 35PCh. 6.2 - Prob. 36PCh. 6.2 - Prob. 37PCh. 6.2 - Prob. 38PCh. 6.3 - Prob. 1PCh. 6.3 - Prob. 2PCh. 6.3 - Prob. 3PCh. 6.3 - Prob. 4PCh. 6.3 - Prob. 5PCh. 6.3 - Prob. 6PCh. 6.3 - Prob. 7PCh. 6.3 - Problems 8 through 10 deal with the competition...Ch. 6.3 - Problems 8 through 10 deal with the competition...Ch. 6.3 - Problems 8 through 10 deal with the competition...Ch. 6.3 - Prob. 11PCh. 6.3 - Prob. 12PCh. 6.3 - Prob. 13PCh. 6.3 - Prob. 14PCh. 6.3 - Prob. 15PCh. 6.3 - Prob. 16PCh. 6.3 - Prob. 17PCh. 6.3 - Prob. 18PCh. 6.3 - Prob. 19PCh. 6.3 - Prob. 20PCh. 6.3 - Prob. 21PCh. 6.3 - Prob. 22PCh. 6.3 - Prob. 23PCh. 6.3 - Prob. 24PCh. 6.3 - Prob. 25PCh. 6.3 - Prob. 26PCh. 6.3 - Prob. 27PCh. 6.3 - Prob. 28PCh. 6.3 - Prob. 29PCh. 6.3 - Prob. 30PCh. 6.3 - Prob. 31PCh. 6.3 - Prob. 32PCh. 6.3 - Prob. 33PCh. 6.3 - Prob. 34PCh. 6.4 - Prob. 1PCh. 6.4 - Prob. 2PCh. 6.4 - Prob. 3PCh. 6.4 - Prob. 4PCh. 6.4 - Prob. 5PCh. 6.4 - Prob. 6PCh. 6.4 - Prob. 7PCh. 6.4 - Prob. 8PCh. 6.4 - Prob. 9PCh. 6.4 - Prob. 10PCh. 6.4 - Prob. 11PCh. 6.4 - Prob. 12PCh. 6.4 - Prob. 13PCh. 6.4 - Prob. 14PCh. 6.4 - Prob. 15PCh. 6.4 - Prob. 16PCh. 6.4 - Prob. 17PCh. 6.4 - Prob. 18PCh. 6.4 - Prob. 19PCh. 6.4 - Prob. 20PCh. 6.4 - Prob. 21PCh. 6.4 - Prob. 22PCh. 6.4 - Prob. 23PCh. 6.4 - Prob. 24PCh. 6.4 - Prob. 25PCh. 6.4 - Prob. 26P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Similar questions
- By using controllability gramian, check if the system representation R(A,B,C) is observable.arrow_forwardFill in only five of the following with a short answer 1. It can assign solution type (minimum or maximum) of control problem through 2. The function of integral control is 3. The system is in critial stable if 4. A third order system with an output equation (y = 2x₁ - x₂) its output matrix is_ 5. A system with state matrix A = [¹ 2] its overshoot value is 6. The stability of the open-loop system depandes onarrow_forward3. The relationship between the input x(t) and output y(t) of a causal continuous-time LTI system is described by the differential equation given below. (a) (b) (c) (d) (e) dy(t) dt + 3y(t) = 2x(t) Find the transfer function H(s) for this system Find the impulse response h(t) for this system. Is this system stable? Give a reason for your answer. Find an expression for the frequency response H() for this system. Find the system output y(t) due to the input x (t) = 5e-²¹u(t).arrow_forward
- 2. A discrete time system has the system function H(z) = z8-3' (a) If the system is stable. What is the region of Convergence of H(2)? (b) For the stable system of part (a), determine h(n), the unit sample response for this system, using any method you choose.arrow_forwardProblem 2 The linearized dynamic model of a certain process is given by i = 3x2 *2 = -2r1 - 4r2 + u i3 = 2r1 – 2r3 %3D y = 13 (a) Determine the matrices A, B,C, and D of the state space representation of the system. (b) Determine the characteristic polynomial of the system. (c) Determine the transfer function of the system. (Any method is permitted)arrow_forwardFor each of the following systems, determine whether the system is (1) linear (2) time invariant (3)memoryless, (4)stable, and (5) casual. (a) y(t) = |x(t)| (b) y(t) = (sin t)x(t) 4+1 (c) y(t) = x(a)da (d) y(t) = dx(1) dtarrow_forward
- 5. If the outmost pole(s) of the z- transfer function H(z) describing the DSP system is(are) on the unit circle on the z-plane pole-zero plot, then the system is : a. unstable b. stable c. marginally stablearrow_forwardConsider the following growing network model in which each node i is assigned an attractiveness a¿ € N+ drawn from a distribution π(a). Let N(t) denote the total number of nodes at time t. At time t = 1 the network is formed by two nodes joined by a link. - At every time step a new node joins the network. Every new node has initially a single link that connects it to the rest of the network. - At every time step t the link of the new node is attached to an existing node of the network chosen with probability II; given by where Z = Ili = ai Z' Σ aj. j=1,...,N(t−1)arrow_forwardUse matlabarrow_forward
- Under what condition system become unstable by routh hurwitz criteria?arrow_forwardreply asaparrow_forwardFor the following proposition, describe (i) a model on which it is true, and (ii) a model on which it is false. If there is no model of one of these types, explain why. ∀x(Px→(Rxx∨∃y(Qy∧Rxy)))arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole