solve ( part h ) onlyyyyy

These are the states vectors of the svsten A=[010;001:560];B=[0;0;1]; C=[100];D=0 Problem: Consider the nonlinear system defined by: x^=[x3+x2x32+x235x15.8x2+x1x2]+001uy=[100]x a) Find the equilibrium points of the system, assume aed-1. b) Linearize the system around the equilibrium points. c) Calculate the cigenvalues of the linearized system using MATLAB and state the stability. d) Check the controllability and observability of the linearired system asing MATLAB. c) Design a full-order state observer with desired eigenvalues of {14,14,16} using the linearined system. f) Simulate the observer designed in part(c) for the nonlinear system using MATt.AB and plot the actual and the estimated states on the same graph assuming x(0)=[301]andx(0)=[000] g) Design a state feedback u=Kx using the linearized system such that the closedloop cigenvalues are placed at {2,4,5}. h) Simulate using MATLAB or SIMULINK the overall closed-loop nonlinear system of the controller and observer designed in c) and e), (observer-based compensator) Consider the nonlinear system defined by: x=x2x3+x2x32+x235x15.8x2+x1x2+001uy=[100]x a) Find the equilibrium points of the system, assume ueq=1. b) Linearize the system around the equilibrium points. c) Calculate the eigenvalues of the linearized system using MATLAB and state the stability. d) Check the controllability and observability of the linearized system using MATLAB. e) Design a full-order state observer with desired eigenvalues of {14,14,16} using the linearized system. f) Simulate the observer designed in part(c) for the nonlinear system using MATLAB and plot the actual and the estimated states on the same graph assuming x(0)=[301]Tandx^(0)=[000]T g) Design a state feedback u=Kx^ using the linearized system such that the closedloop eigenvalues are placed at {2,4,5}. h) Simulate using MATLAB or SIMULINK the overall closed-loop nonlinear system of the controller and observer designed in c) and e), (observer-based compensator)