- For the systemdX(t)dt= [₁¹₁]X(t), check whether the system is asymptotically stable usingLyapunov theorem

Answered: Image /qna-images/answer/2bd9db16-f19a-4834-8554-d3ab36921e77.jpg

Answered: - For the system dX(t) dt Lyapunov…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.9: Properties Of Determinants

Problem 44E

See similar textbooks

Similar questions

Find the linearization at x = a. f(x) = ) = — - ₁a = 1 x2, = 7
Consider the linear system ÿ' [₁ 3 -5 -5 2 -3 y.
Which of the following functions V(y1, y2) is a Lyapunov function for the dynamical system y₁ = (4-₁)ex, y2 = y²-y²y₂ Select one: a. V(v₁.32) = -4+(2-1)³ b. V(v₁.y2) = -²³ +²² c. V(v₁.92) = ₁ + y/² C. Od. V(y₁, y2) = (y₁ - 4)4+ (y2 - 1)²
Is the set of functions linearly independent or linearly dependent? In the linearly dependent case, find nonzero constants C₁,..., C such that c₁y₁ + ... + £¥n = 0. 31. = = 1,y (0) =0. c) y(0) = 1, y' (0) = 0, y"(0) = -1. 32 {x1,2x+1, 3x}.
Let dx/dt = x2y3 dy/dt = -x - y - (xy4)/2 be a dynamical system. Is L(x,y) = (x2)/2 + (x2y4)/4 a proper Lyapunov function?
1. Is L = {1 − 2x + 3x^2, x − 2x^2, 2 − 5x + 8x^2} linearly independent? If yes, show why. If not, show a dependence relationship. Is L = {1 + 2x + 2x^2, x − 2x^2, −2 − 3x − 5x^2} linearly independent? If yes, show why. If not, show a dependence relationship.
f(t) = Fit a linear function of the form f(t) = co + C₁t to the data points (-2, 9), (0, -3), (2, -27), using the least squares method.
Consider the system below * + dx3 + kx = 0 Show that V(x) = (kx² + x²) is a Lyapunov function. Is the system Lyapunov stable, asymptotically stable?
ii-Consider the nonlinear system *+ x³ + sinx = 0. Assume that V(x) = x + (x + x)² + 2f. Find f such that the origin is globally asymptotically stable.
: Find the orthogonal trajectories of the family of curves y4 = kx³. (A) ²³ + 3x² = C (B) 2y³ + 2x² = C с (F) 2y³ + {/x²³ = C (G) ¾ y² + x² = C (C) y² + 2x² = C D) y² + x³ = c ) ² + 2x² = C 5 (H) H²³² + x³ = c C
Prove that if y1 and y2 are linearly independent solutions to thehomogeneous, then the functions y3 = y1 + y2 and y4 = y1 - y2 are also linearly independent solutions.
A system of the type i = f(x), f(x) = -gradV(x), is called a gradient system. Investigate the stability of a fixed point. (Hint: Compute the Lie derivative of V)

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Calculus For The Life Sciences

Calculus

ISBN:

9780321964038

Author:

GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:

Pearson Addison Wesley,

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Calculus For The Life Sciences

Calculus

ISBN:

9780321964038

Author:

GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:

Pearson Addison Wesley,

SEE MORE TEXTBOOKS

- For the system dX(t) dt Lyapunov theorem =[₁₁]X(t), check whether the system is asymptotically stable using