ME-GY 6703 Linear Control Theory and Design, Spring 2024
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
ME-GY 6703 Linear Control Theory and Design, Spring 2024
Homework Assignment 1
1. Given the matrix A below, compute such that its entry on the first row and first column ()11 is equal to 4.
2. Given the matrix A below, compute eA via diagonalization.
3. If A(t) is a continuously-differentiable N × N matrix function that is invertible at each t, show that
4. Compute the spectral norm of the following matrices:
5. Consider the nonlinear state equation, with a, b, c, d, f nonzero parameters,
Show that the origin is an equilibrium and derive a linearized model to describe perturbations in the vicinity of the origin.
6. Linearize the nonlinear state equation
about the nominal trajectory arising from (0) = 0, (0) = 1, and (t) = 1 for all t ≥ 0. Is the linear system time-varying?
2024-02-18