Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit

EE 4233 - Spring 2021

Exam 2

Problem 1: Observability

a: Check if the following system is observable

b: Check if the following system is observable

c: Consider the system

Find an initial condition, x(0), such that x(0) ≠ 0 and y(t) = 0 for all t ≥ 0.

d: Show that the following system is not observable

Problem 2: Minimal Realizations

a: Find a minimal realization of the following system:

b: Check if the following realization is minimal:

c: Consider a single-input, single-output system given by:

Is there a vector B that makes this a minimal realization?

d: For the system from part c, find a vector B so that the minimal realization has state dimension 1.

Problem 3: Stability

a: Is the origin of the following system an asymptotically stable equilibrium?

Explain your answer.

b: Check if the following system is BIBO stable.

c: Determine if the following system is BIBO stable:

d: Consider a system of the form

where the eigenvalues of A have negative real parts and g is a constant non-zero vector.

Find limt→∞ x(t).