A non-linear system is defined by the following set of differential equations: X₁₂ =−x₁ + x₂ + 2x²2² *, =−2X_X, +X, tu y

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A Non Linear System Is Defined By The Following Set Of Differential Equations X X X 2x 2 2x X X Tu Y 1 (85.36 KiB) Viewed 34 times

A non-linear system is defined by the following set of differential equations: X₁₂ =−x₁ + x₂ + 2x²2² *, =−2X_X, +X, tu y = x₁ a) Show that (x₁,x₂;u) = (0,0;0) is one equilibrium point of the above system and linearise it at this equilibrium point. b) For the linearised system of part Q3.a), do the following: i) Compute the eigenvalues, left and right eigenvectors, and the dyadic decomposition of the state transition matrix. ii) Investigate the internal and external stability properties of the linearised system. Hence, comment about its controllability and observability properties as well.