Question 1 (a) State the controllability and observability rank criteria for linear state space control systems of the f

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Question 1 A State The Controllability And Observability Rank Criteria For Linear State Space Control Systems Of The F 1 (57.64 KiB) Viewed 19 times

Question 1 (a) State the controllability and observability rank criteria for linear state space control systems of the form: x(t) = Ax(t) + Bu(t), x(0) = X, y(t) = Cx(t) for appropriate matrices A, B and C. [5 marks] Now consider the nonlinear control system in state space form given by x₁ = 2x²x₂ - 4x² x₂ =−x₁x² + 5x² + 4u with output function given by y = x₁ + 5x₂ (b) Show that, for the constant steady state input level u(t) = 2, there exists only one real steady state. [6 marks] (c) Obtain a linearisation of the nonlinear system valid for small perturbations about this steady state and steady state input. [8 marks] (d) Determine whether this linearisation is controllable and whether it is observable using the controllability and observability rank criteria, or otherwise. [6 marks]