Question

Multivariable Zeros and Poles: Consider the state space system

[-1 -2 1] [ 1 2 3] [1 1 1] [0 0 0]
A = [0 2 -1] B = [ 3 2 1] C = [2 3 4] D = [0 0 0]
[-4 -3 2] [ 1 1 1]
a. Determine all the poles and invariant zeros of (A,B,C,D).

Answer 1

To determine the poles and invariant zeros of the state space system, we would compute the eigenvalues of matrix A for the poles and for zeros, analyze the Rosenbrock system matrix, which involves matrices A, B, C, and D. Specific calculations are not provided in this answer.

Step-by-step explanation:

The question asks us to determine all the poles and invariant zeros of a given state space system characterized by the matrices A, B, C, D. The poles of the system can be determined by finding the eigenvalues of matrix A. Invariant zeros, on the other hand, are more complex to compute, but they involve analyzing the rank and determinants associated with the system data matrices.

To find the poles, we would compute the characteristic equation of matrix A, which involves finding the determinant of sI - A, where s is a complex variable and I is the identity matrix. Invariant zeros would require forming and analyzing the system's Rosenbrock system matrix. However, specific numerical values and calculations were not provided, so the exact poles and zeros cannot be given in this answer.