Consider an n-dimensional linear time-invariant system x Ax+ Bu. = a) What is the state space?...

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Consider an n-dimensional linear time-invariant system x Ax+ Bu. = a) What is the state space? b) c) Suppose that u E R². What are the dimensions of matrices A and B? Discretize the system into discrete time with step size 8. You need to express x((k+1)8) in terms of A, B, 8, x(k8), u(k8). To make the notation easier to read, you can use x[k + 1] instead of x((k+1)8) to denote the discrete-time state and express x[k +1] in terms of x[k]; note that you still need to consider the impact of 8. d) Suppose that we use a linear controller u(x) = -Kx. Write the difference equation for the discretized system; i.e., write how to obtain x[k+1] from x[k]. Find x[k] in terms of A, B, K and the initial condition x[0] = x₁ € R¹. Consider an n-dimensional linear time-invariant system x Ax+ Bu. = a) What is the state space? b) c) Suppose that u E R². What are the dimensions of matrices A and B? Discretize the system into discrete time with step size 8. You need to express x((k+1)8) in terms of A, B, 8, x(k8), u(k8). To make the notation easier to read, you can use x[k + 1] instead of x((k+1)8) to denote the discrete-time state and express x[k +1] in terms of x[k]; note that you still need to consider the impact of 8. d) Suppose that we use a linear controller u(x) = -Kx. Write the difference equation for the discretized system; i.e., write how to obtain x[k+1] from x[k]. Find x[k] in terms of A, B, K and the initial condition x[0] = x₁ € R¹.

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a The state space of the system is the set of all possible states that the system can be in In this ... View the full answer