2 The state space presentation of a system can be captured by four Matrices A.,B,C, and D. 3 -2 1 0 a) Is this system stable? b) What is the order of the system? 2 The state space presentati...
(Full Order Observer). Given the following state space equations =1-5-251-1 -1 0 1 0 CID | a) Determine if the system is stable. b) Is the system Observable? Detectable? c) Design a full order observer that places the estimator-error poles at {-5±5 d) Check the entire set of eigenvalues of the estimator.
7. Consider the following matrices 2 3-1 0 1 A=101-2 3 0 0 0-1 2 4 2 3 -1 B-101-2 0 0-1 2 3 -1 0 c=101-2 3 For each matrix, determine (a) The rank. (b) The number of free variables in the solution to the homogeneous system of equa- tions (c) A basis for the column space d) A basis for the null space for matrices A and HB e) Dimension of the column space (f) Nullity (g) Does...
4.44 Find the A, B, C, and D state matrices for a composite system of Figure 3.27 of Sec. 3.5. ubsystemm H,(s) = (s + 2)/(s2 + 4s + 3). and sub Vi u, → Subsystem 1 Subsystem, 1 Figure 3.27
2. (6 points). Consider a state space system: C1 =22 22 = - 2.c 1 - 3.02 y=21 +22 Eco with Xo = (-1,1). (a) Specify the state space matrices (A,B,C,D). (b) Compute the matrix exponential eAl using similarity transformation. (e) Find the complete state response (solution of the SS system x(t)) if u(t) = 1. (d) Find the output response y(t) = Cx(t).
State Space 37. Given the following state-space re- presentation of a system, find Y(s): [Section: 4.10] SS *= [ __ __}}x+ [1]sin 31 y = [1 2]x; x(0) = Pi)
find the eigen space of 4a and 4c Find the characteristic equations of the following matrices 4. (a) 「 4 0 1 -2 1 0 -2 0 1 (b) [3 0-5 1 1-2 11 1-2 0 (c) 19 5 -4 (d) -1 0 11 -1 3 0 -4 13 1 (e) 5 0 11 ind bases for the eigenspaces of the matrices in Exercise 4 6. Find the characteristic equations of the following matrices 4. (a) 「 4 0 1...
(1 point) Find a basis for the column space of 0 A = -1 2 3 3 - 1 2 0 - 1 -4 0 2 Basis = (1 point) Find the dimensions of the following vector spaces. (a) The vector space RS 25x4 (b) The vector space R? (c) The vector space of 6 x 6 matrices with trace 0 (d) The vector space of all diagonal 6 x 6 matrices (e) The vector space P3[x] of polynomials with...
[1 0 O1[i 2 0 3 6. (4) Let A 3 1 0l0 0 3 1. Without multiplying the matrices, 0 -1 1110 0 0 0 (a) Find the dimension of each of the four fundamental subspaces. b have a solution? (b) For what column vector b (b, b2, ba)' does the system AX (c) Find a basis for N(A) and for N(AT). [1 0 O1[i 2 0 3 6. (4) Let A 3 1 0l0 0 3 1. Without...
Exercise 5.5. Consider the linear system 2 as in (5.44) with A-4 0 C [1 0 -1 4 1 a. Show that the system is not (internally) asymptotically stable b. Show that the system is both controllable and observable. c. Find matrices F e R1x2 and GE R2x1 such that o(A+ BF) C C_ and o (A GC) C C_ d. Find matrices (K, L, M, N) such that the feedback controller w(t) Kw(t) Ly(t) u(t) Mw(t)Ny(t) is internally stabilizing...
A system G has its model in state-space as: C [2 0] 1. Assuming a unity feedback is constructed for G, find the phase margin of this feedback system 2. Assuming a state-feedback is applied to G, it is possible to find a state feedback gain K such that the closed-loop system carries poles at -1 and -2? If yes, what is K?