% Fall'06 - Spring'07 16.01-16.04 MATLAB Tutorials: Linear Systems
% Instructor: Violeta Ivanova, violeta@mit.edu
% Faculty: Mark Drela, Stephen Hall, Wes Harris, Ian Waitz

% Example 1: Linear Systems: Eigenvalues and Eigenvectors
% This exercise is based on S. Hall's Signals and Systems lectures.

% C1. State space linear equations: x' = Ax
% If  x = (v; i), create the matrix A for the following system:
% dv/dt = -1/2*v - 2*i
% di/dt =  1/2*v - 3*i



% C2. Define vector x0 for initial conditions: v(0) = 2 and i(0) = 1



% C3.  Compute eigenvalues and eigenvectors of the matrix A
% Hint: use function EIG with option 'nobalance' for non-symmetric A



% Compute a column vector lambda including the two eigenvalues:


% Compute two column eigvectors eigvec1 and eigvec2:


      
% C4. Compute v(t) and i(t) for 0 < t < 5s
% Hint: the solution has exponential form - see handout for formula

% Compute the coefficients' vector a from the initial conditions x0
% Hint: Use operator \ to solve equation x0 = eigenvectors * a




% C5. Plot v(t) and i(t) vs. time t