Question

Consider the following system:

x˙(t)=[0−21−3]x(t)+[01]u(t)
y(t)=[10]x(t)

with x(0)=(10)
Using the I sim function obtain and plot the system response (for x1(t)
and x2(t) ) when u(t)=0

Answer 1

The student is tasked with finding the response of a linear system with zero input using the state-space representation and MATLAB's 'lsim' function, leading to plots of the state variables over time.

Step-by-step explanation:

The student's question is about analyzing the response of a linear time-invariant system described by differential equations when the input u(t) is zero. The state-space representation includes a matrix that defines the system dynamics and initial conditions for the state variables x1(t) and x2(t).

To solve for the system's response in terms of x1(t) and x2(t) when u(t) = 0, we must consider the homogeneous part of the system. The solution involves finding the state transition matrix, applying it to the initial conditions, and obtaining the response over time. This process would typically be performed using MATLAB's 'lsim' function to simulate the system response, followed by plotting the results.