Consider the following dynamical system equation: Assume that the system is sing

Question

Consider the following dynamical system equation: Assume that the system is single input-single output, and of dimension 8. Thus, A is an 8 8 matrix, B is 8 1, and C is 1 8. Assume also that the system also has the following properties: Rank U 5, Rank V 3, where U is the controllability matrix, and V is the observability matrix of the system. How many controllable states are there in the system? How many observable states are there? What is the minimum and maximum number of states that this system can have which are BOTH controllable and observable? Under what conditions can we stabilize this system using full state feedback? Assume that the intersection of the span of U and the nullspace of V is a linear subspace of dimension 3. After Complete canonical decomposition, the system will be in the form as shown below. Identify the sizes of the following matrix blocks: What is the order of the system transfer function, assuming the information in part d?

Explanation / Answer

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