1. Consider the system described by i(t) = u(t) – sin (x(t)) y(t) = u(t) + cos (x(t)) a) Find all equilibrium points of the system. b) For each equilibrium point, determine whether or not the equilibrium point is (i) stable in the sense of Lyapunov; (ii) asymptotically stable; (iii) globally asymptotically stable. Explain your answers. c) Determine whether or not the system is bounded-input bounded-output stable. Explain your answer.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
1. Consider the system described by
i(t) = u(t) – sin (x(t))
y(t) = u(t) + cos (x(t))
%3D
a) Find all equilibrium points of the system.
b) For each equilibrium point, determine whether or not the equilibrium point is (i) stable in the
sense of Lyapunov; (ii) asymptotically stable; (iii) globally asymptotically stable. Explain
your answers.
c) Determine whether or not the system is bounded-input bounded-output stable. Explain your
answer.
Transcribed Image Text:1. Consider the system described by i(t) = u(t) – sin (x(t)) y(t) = u(t) + cos (x(t)) %3D a) Find all equilibrium points of the system. b) For each equilibrium point, determine whether or not the equilibrium point is (i) stable in the sense of Lyapunov; (ii) asymptotically stable; (iii) globally asymptotically stable. Explain your answers. c) Determine whether or not the system is bounded-input bounded-output stable. Explain your answer.
Expert Solution
steps

Step by step

Solved in 4 steps

Blurred answer
Knowledge Booster
Differential Equation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,