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A non-linear system is defined by the following set of differential equations: xI=−1x+x2+2x21I2=−2x1x2+x2+uy=x1
Posted: Thu Jul 14, 2022 2:39 pm
by answerhappygod
- A Non Linear System Is Defined By The Following Set Of Differential Equations Xi 1x X2 2x21 I2 2x1 X2 X2 Uy X1 1 (40.97 KiB) Viewed 40 times
A non-linear system is defined by the following set of differential equations: xI=−1x+x2+2x21I2=−2x1x2+x2+uy=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. [7 marks] 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. [12 marks] ii) Investigate the internal and external stability properties of the linearised system. Hence, comment about its controllability and observability properties as well. [6 marks]