Let's find the solution: |x(t) = etxo, y(t) = Cx(t) = Cetxo to the following LTI...

Transcribed Image Text:

Let's find the solution: |x(t) = etxo, y(t) = Cx(t) = Cetxo to the following LTI system with no input which has some initial condition: [10 -62.9₁ -12] , C₁ = [1 2],x(¹) = A₁ = Hints Note that the following system is diagonalizable. Basically, matrix A₁ is already in diagonal form. In this case, the solution will be straightforward, as we will need to find the eigenvalues and the eigenvectors associated with the system and perform eigenvalue decomposition before using the matrix exponential capability to find the solution to the ODE's. 0 A₁ ¹ = [1 2] ₁G₁ = [¹ 2] ₁x¹ = [121] Let's find the solution: |x(t) = etxo, y(t) = Cx(t) = Cetxo to the following LTI system with no input which has some initial condition: [10 -62.9₁ -12] , C₁ = [1 2],x(¹) = A₁ = Hints Note that the following system is diagonalizable. Basically, matrix A₁ is already in diagonal form. In this case, the solution will be straightforward, as we will need to find the eigenvalues and the eigenvectors associated with the system and perform eigenvalue decomposition before using the matrix exponential capability to find the solution to the ODE's. 0 A₁ ¹ = [1 2] ₁G₁ = [¹ 2] ₁x¹ = [121]