1. Compute the Jordan canonical form, and compute a matrix V such that VAV is in the Jordan canonical form: A) 0 O 0 2 0 BY -2 0 1/3 -5/3Question 3. A control system has the transfer function Y(s) = 3(s + 3)(s + 4) 3s2 + 21s + 36 = R(s) (s + 1)(s +2)(s+ 5) s' +852+17s +10 (1) Draw the signal-flow graph state model in (a) phase variable canonical form (5 marks) (b) input feedforward canonical form (5 marks) (c) diagonal canonical form (5 marks) x(t) = Ax(t) + Br(t) (2) Find the state space representation for each canonical form y(t) = Cx(t) + Dr(t) in (1). (15 marks)1. Consider a birth and death process with 4 attainable states: (0, 1, 2, 3). The steady state probabilities of these states are PO, PI, P2, and P3. The birth and death rates are summarized in the below table: State Birth Rate Death Rate 0 NNN 0 a) Construct the rate diagram for this birth and death process. b) Develop the balance equations c) Solve these equations to find PO, PI, P2, P3 (steady state probabilities). d) Calculate L.Determine Irvhether the value is a discrete random variable. continuous random variable. or not a random variable. a. The distance a baseball travels in the air after being hit b. The number of people in a restaumnt that has a capacity of 100 c The gender of college students d. The number oftextbook authors novv sitting at a computer e. The number of bald eagles in a country f. The exact time it takes to evaluate 2? plus Ha. Is the distance a baseball travels in the air alter being hit a discrete randomvariable. a continuous random variable. or not a random variable? A. it is a continuous random variable. B. It is a discrete random variable. C. It is not a random variable. b. Is the number of people in a restaurant that has a capacity of 106 a discrete random variable. a continuous random variable, or not a randomvariable? A. It is a diso'ete random variable. E. It is a continuous random variable. C. It is not a random variable o Is the gender of college students a discrete random variable. a continuous mndom variable. or not a random variable? A. ll is a discrete random variable. B. ft is a continuous random variable. C. it is not a random variable. d. Isthe number oftextboolc authors nov.r sitting at a computera discrete random variable. a continuous random variable. or not a random variable? A. It is a continuous random variable. B. It is a discrete random variable. C. It is not a random variable. e. Is the nu mberof bald eagles in a country a discrete random variable. a continuous random variable. or not a random variable?A. It is a continuous random variable. B. It is a discrete random variable. (1 it is not a random variable. f. Is the exact time ittalces to evaluate 2? plus T2 a discrete randomvariable. a continuous random variable. or not a random variable? A. It is a discrete random variable. EL it is a continuous random variable. C. it is not a random variable. Click to select your
