Using MATLAB and classical not Laplace methods only solve fo

Using MATLAB and classical (not Laplace) methods only, solve for state-transition matrix, the state vector, and the output of the system represented here.

Solution

% Given -------------------------------------------------------------------
A = [0 1;-1 -5];
B = [0;0]
C = [1 2];
D = [0];
X = [1;0];
I = [1 0;0 1];
sys = ss(A,B,C,D);
% Create Symbolic Object s ------------------------------------------------
syms s;
% Assume ------------------------------------------------------------------
% MatrixSTM as state transition matrix order 2x2 with elements of inverse
% of resilient matrix ILT.
% -------------------------------------------------------------------------
ILT = (((s*I) - A)^-1);
MatrixSTM=ilaplace(ILT);
% Display State Transition Matrix -----------------------------------------
disp(\'State Transition Matrix is = \');
disp(MatrixSTM);
% Calculating Zero Input Response -----------------------------------------
zeroResP = MatrixSTM*InitialX