( Consider a dynamic system described by = f(x, u) where x ER is the system state, and u ER is the input. Given is ux³ + 2x + u f(x, u) = Note that x* = 0, u* = 0 is an equilibrium of this system The system's control input is given by the control law u = -kx. For which values of k will the closed-loop system be stable (in the sense of Lyapunov) at the equilibrium?
( Consider a dynamic system described by = f(x, u) where x ER is the system state, and u ER is the input. Given is ux³ + 2x + u f(x, u) = Note that x* = 0, u* = 0 is an equilibrium of this system The system's control input is given by the control law u = -kx. For which values of k will the closed-loop system be stable (in the sense of Lyapunov) at the equilibrium?
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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![Consider a dynamic system described by i = f(x,u) where x E R is the system state, and u E R
is the input. Given is
f(x, u)
ux + 2x + u
Note that x* = 0, u* = 0 is an equilibrium of this system
The system's control input is given by the control law u = -kx. For which values of k will the closed-loop
system be stable (in the sense of Lyapunov) at the equilibrium?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5277c1f3-9802-4713-b096-bbd0b3c2e8c8%2F0e63e0e5-826a-4d67-b807-f8074b03692d%2Fbink9df_processed.png&w=3840&q=75)
Transcribed Image Text:Consider a dynamic system described by i = f(x,u) where x E R is the system state, and u E R
is the input. Given is
f(x, u)
ux + 2x + u
Note that x* = 0, u* = 0 is an equilibrium of this system
The system's control input is given by the control law u = -kx. For which values of k will the closed-loop
system be stable (in the sense of Lyapunov) at the equilibrium?
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