2. (1 (2 (3) (4) (5) Homework 11 1. Consider a linear time invariant system, А A=[1²_²3];B =[²₁];C=[-1 -2];D=1 (1) For
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Homework 11 1. Consider a linear time invariant system, А A=[1²_²3];B =[²₁];C=[-1 -2];D=1 (1) For the matrix M = = [1¹1]₁₁ calculate M-¹ (2) Introduce the new state variable q that is defined as q = Mx, determine the matrices A, B, C and D, for the state equation after coordinate transformation. q=A₁q+B₁u y₁ = C₁q+D₂u 9 (3) Write down the state equation (two differential equations about state variables q, and q₂) and output equation (one algebraic equation for output ya) (4) Based on the state equations obtained in question (3), determine the state variable (q, or q₂) that cannot be controlled by the input u. x(t) = Ax+ Bu y(t) = Cx+ Du