Linear State Space Control Systems

Q2. For given state space model 110 A = 9 .0 4 -4 10 0 0 0] B = 101 C = [5 6 0], D = [3] a) Investigate the controllability using PBH eigenvector test and, if there exists, find the uncontrollable modes. b) Investigate the observability using PBH rank test and, if there exists, find the unobservable modes. c) Is your state space model minimal, why? If not, find its minimal state space representation. d) Check your results with MATLAB, etc. Q2. For given state space model 110 A = 9 .0 4 -4 10 0 0 0] B = 101 C = [5 6 0], D = [3] a) Investigate the controllability using PBH eigenvector test and, if there exists, find the uncontrollable modes. b) Investigate the observability using PBH rank test and, if there exists, find the unobservable modes. c) Is your state space model minimal, why? If not, find its minimal state space representation. d) Check your results with MATLAB, etc