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Problem 1. Consider the following transfer matrix s+1 T(S) = Let G=TO -6-s s+1 Find the...
uestionI. A system is represented by the following transfer function G(s)- (s+1)/(s2+5s+6) 1) Find a state equation and state transition matrices (A,B, C and D) of the system for a step input 6u(t). ii) Find the state transition matrix eAt) ii) Find the output response of system y(t) to a step input 6u(t) using state transition matrix, iv) Obtain the output response y(t) of the system with two other methods for step input óu(t). Question IV. A system is described...
I need help with parts c and d of this question. Some concept
clarification would be great.
3. Consider the following matrix A= 3 6 (a) Compute AAT and its eigenvalues and unit eigenvectors. (b) Find the SVD by computing the matrices U, V, Σ (c) From the u's and v's in (b), write down orthonormal bases for all four fundamental subspaces (i.e., row space, column space, null space, left null space) of the matrix A. (d) Compute the pseudoinverse...
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2 Consider the transfer function V (s) Put the system in state space form. Compute the eigenvalues of the resulting A matrix. Is the system stable?
2 Consider the transfer function V (s) Put the system in state space form. Compute the eigenvalues of the resulting A matrix. Is the system stable?
Need help with linear algebra problem!
Let S be a symmetric, 2 x 2 matrix. Let û1) and ût2) be orthogonal eigenvectors of S with corresponding nonzero eigenvalues A1 and X2. Show that if v E R2 is a vector such that û1)Su = 0, then 5 = Bû(2) for some B 0.
Let S be a symmetric, 2 x 2 matrix. Let û1) and ût2) be orthogonal eigenvectors of S with corresponding nonzero eigenvalues A1 and X2. Show that...
I need help with this question. Some clarification would be
great.
3. Consider the following matrix A= 3 6 (a) Compute AAT and its eigenvalues and unit eigenvectors. (b) Find the SVD by computing the matrices U, V, Σ
3. Consider the following matrix A= 3 6 (a) Compute AAT and its eigenvalues and unit eigenvectors. (b) Find the SVD by computing the matrices U, V, Σ
Consider a 2x2 transition matrix P consisting of column vectors [a c] and [b d]. The matrix P has two eigenvalues: 1 and k. Find the value of k in terms of the elements of the matrix P and place constraints of the values of k. Calculate eigenvectors for each eigenvalue and hence write down the matrix S whose columns are the eigenvalues of P.
Problem 2 (Eigenvalues and Eigenvectors). (a) If R2 4 R2 be defined by f(x,y) (y,x), then find all the eigenvalues and eigenvectors of f Hint: Use the matrix representation. (b) Let U be a vector subspace (U o, V) of a finite dimensional vector space V. Show that there exists a linear transformation V V such that U is not an invariant subspace of f Hence, or otherwise, show that: a vector subspace U-0 or U = V, if and...
Problem 2. Let 1 1-i 1+i 0 T= (a) Verify that T is hermitian. (b) Find its eigenvalues and corresponding (normalized) eigenvectors (d) Construct the unitary diagonilizing matrix S and explicitly evaluate STS-1
Problems: Consider the following system, G11(s) G12(8) G21 (s) G22(s) S+I S+2 G(s) 1S+2 s+1 and answer the following questions 1. Find the poles and zeros for each SISO transfer function G1 (s), G12(s), G21 (s) and G22(s) 2. For each SISO transfer function, eg, Yu (s) = G11(s)U1 (s), calculate a state space realization. 3. Explain how to obtain G(s) by connecting the four SISO transfer functions from 2 and calculate a state space realization for G(s) based on...
Here is the matrix mentioned in the problem:
7) Change (23 pts) Diagonalization of a matrix. For the matrix from the last problem. a) (6 pts) Find the eigenvalues of A b) (6 pts) Find the eigenvectors of A, Choose x1=1 for the first element of both eigenvectors. c) (4 pts) Is this system stable? What type of damping does it have? d) (2 pts) Find the diagonal matrix D corresponding to A. e) (1 pts) Find D3, use actual...