Q4. Given three agents with states x¡, i = (1,2,3). The agents are connected together and they updat their states in continuous domain based on the following rule: 3 ž(t) = (x(0) – x,(0). j=1 a) Represent the state progress as a linear system i = Ax, where x = [x1, X2, X3]" and with th initial condition x(0) = [x1(0), x2(0), x3(0)]'. b) Analyze the properties of A, i.e., find its eigenvalues, eigenvectors, determinant, etc. c) Find the Jordan normal form of the matrix A. Find e4t analytically. Write down the analytica solution of x(t) and calculate lim x(t). Analyze behavior of the system as time goes to infinity t→∞ How would the state progress with time?

Q4. Given three agents with states x¡, i = (1,2,3). The agents are connected together and they updat their states in continuous domain based on the following rule: 3 ž(t) = (x(0) – x,(0). j=1 a) Represent the state progress as a linear system i = Ax, where x = [x1, X2, X3]" and with th initial condition x(0) = [x1(0), x2(0), x3(0)]'. b) Analyze the properties of A, i.e., find its eigenvalues, eigenvectors, determinant, etc. c) Find the Jordan normal form of the matrix A. Find e4t analytically. Write down the analytica solution of x(t) and calculate lim x(t). Analyze behavior of the system as time goes to infinity t→∞ How would the state progress with time?