A state space linear system is shown below. Use Matlab to solvethe following problems.
Requirement for project report: (1) Results; (2) Matlabcode.
dx1/dt=-x1(t)+u(t)
dx2/dt=x1(t)-2×2(t)-x3(t)+3u(t)
dx3/dt=-3×3(t)
y(t)=-x1(t)+2×2(t)+x3(t)+u(t)
(1) Compute the analytical expression of transition matrix forthe above linear system using Matlab.
(2) Assume the system has zero input (u(t)=0) and initial statex(0)=[1;1;1]. Using the transition matrix obtained, compute thesystem’s output (analytical solution) y(t), and plot the output asa function of time (t within 0 to 10).
Solution