Given three agents with states �O, � = (1,2,3). The agents are connected together and they updatetheir states in continuous domain based on the following rule: Q4. Given three agents with states xi, i = (1,2,3). The agents are connected together and they updatetheir states in continuous domain based on the following rule:3*;(t) =Ax, where x = [x1,x2, X3]" and with thea) Represent the state progress as a linear system i =initial condition x(0) -b) Analyze the properties of A, i.e., find its eigenvalues, eigenvectors, determinant, etc.Find the Jordan normal form of the matrix A. Find e4t analytically. Write down the analyticalsolution of x(t) and calculate lim x(t). Analyze behavior of the system as time goes to infinity.[x1(0), x2(0), x3(0)]".%3DHow would the state progress with time?d) Simulate the system on Simulink with x1(0) = 2, x2(0) = -4, x3(0) = 1. Comment on theresult. Submit the plot of your system. (Simulate the system sufficiently long time to see theactual behavior!)Note: The matrix L = -A is called the Laplacian matrix.

Solution of part (a): It is given that xi.(t)=∑j=13xjt-xit. So,…

Q4. Given three agents with states xi, i = (1,2,3). The agents are connected together and they update their states in continuous domain based on the following rule: 3 ž,(t) = (*, (t) – x,(t). j=1 Ax, where x = [x1,x2, X3]" and with the a) Represent the state progress as a linear system i initial condition x(0) = [x1(0), x2(0), x3(0)]". %3D %3D 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 analytical 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?