Homework Answers
Asymptotically stable means poles of function should be left side of plane.
Asymptotically unstable means at least one pole of the function is right side of the plane.
Asymptotically marginally stable means at least one pole at origin and other poles should be left side of the plane.
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Each of the following equations specifies an LTID system. Determine whether these systems are asymptotically stable, un...
6. Find h[k], the unit impulse response of the systems described by the following equations: a)...
6. Find h[k], the unit impulse response of the systems described by the following equations: a) y[k] + 3y[k – 1] + 2y[k – 2] = f[k] +3f[k – 1] +3f[k – 2] b) yk + 2 + 2y k + 1] + yſk] =2fk + 2] – fk + 1] c) y[k] - yſk – 1] + 0.5y[k – 2] = f[k] + 2f[k – 1]
For each of the following discrete systems described by either its transfer function or its unit...
For each of the following discrete systems described by either its transfer function or its unit impulse response, determine if the system is asymptotically stable, marginally stable, or unstable 1. z +1 / I. 1.5% 1 0.5 (b) Mn]:e-n sin(m)11[n]
For each of the following systems, determine whether the system is (1) stable
For each of the following systems, determine whether the system is (1) stable, (2) causel, (3) linear, (4) time invariant, and (5) memoryless.
Use the Lyapunov equation method to determine whether the following system is asymptotically stable:
Use the Lyapunov equation method to determine whether the following system is asymptotically stable:
Dasi 1. For each of the following systems, determine whether the system is (1) stable, (2)...
Dasi 1. For each of the following systems, determine whether the system is (1) stable, (2) causal, (3) linear, (4) time invariant, and (5) memoryless: (a) 7(x[n]) = g[n]X[n] with g[n] given (b) (x[n]) = x=no x[k] n20 (c) 7(x[n]) = (d) T(x[n]) = x[n - nol + x[k] (e) T(x[n]) = ex[n] (f) T(x[n]) = ax[n] + b (g) T(x[n]) = x[-n] (h) T(x[n]) = x[n] + 3u[n + 1).
For each of the following systems: (i) Find the general solution by using eigenvalues and eigenvectors....
For each of the following systems:
(i) Find the general solution by using eigenvalues and
eigenvectors.
(ii) State whether the origin is stable, asymptotically stable,
or unstable.
(iii) State whether the origin is a node, saddle, center, or
spiral.
For each of the following systems: (i) Find the general solution by using eigenvalues and eigenvectors. (ii) State whether the origin is stable, asymptotically stable, or unstable. |(iii) State whether the origin is a node, saddle, center, or spiral. Problem 1:...
#3 Find the fixed points and determine whether each ws Vottraiting (asymptotically stable) or a) S09243-**...
#3 Find the fixed points and determine whether each ws Vottraiting (asymptotically stable) or a) S09243-** b) xxx c) *) 2 x?- repelling
#3 Find the fixed points and determine whether each Vattraiting (asymptotically stable) or repelling a) SX12...
#3 Find the fixed points and determine whether each Vattraiting (asymptotically stable) or repelling a) SX12 43-X b) xax =) (A) = *-*
3. Show tha the system of equations where r r2 + y2 has a limit cycle at r - To for each ro such ...
3. Show tha the system of equations where r r2 + y2 has a limit cycle at r - To for each ro such that F(ro) = 0 and F,(m)メ0. The orbit is called asymptotically orbitally stable if F(ro) >0 and unstable if F(ro)0. For the case when F(r)r2)(2- 4r 3) find all limit cycles, determine the orbital stability, and sketch the orbits in the phase plane.
3. Show tha the system of equations where r r2 + y2 has...
2. (Chapter 2). A linear, time-invariant, continuous-time (LTIC) system with input f(t) and output y(t) is specified by the differential equation D2(D +1)y(t) (D - 3)f(t) Find the characteristic poly...
2. (Chapter 2). A linear, time-invariant, continuous-time (LTIC) system with input f(t) and output y(t) is specified by the differential equation D2(D +1)y(t) (D - 3)f(t) Find the characteristic polynomial, characteristic equation, characteristic root(s), and characteristic mode(s) of this system. a. b. Is this system asymptotically stable, marginally stable, or unstable? Justify your answer.
2. (Chapter 2). A linear, time-invariant, continuous-time (LTIC) system with input f(t) and output y(t) is specified by the differential equation D2(D +1)y(t) (D - 3)f(t)...
6. Find h[k], the unit impulse response of the systems described by the following equations: a) y[k] + 3y[k – 1] + 2y[k – 2] = f[k] +3f[k – 1] +3f[k – 2] b) yk + 2 + 2y k + 1] + yſk] =2fk + 2] – fk + 1] c) y[k] - yſk – 1] + 0.5y[k – 2] = f[k] + 2f[k – 1]
For each of the following discrete systems described by either its transfer function or its unit impulse response, determine if the system is asymptotically stable, marginally stable, or unstable 1. z +1 / I. 1.5% 1 0.5 (b) Mn]:e-n sin(m)11[n]
Use the Lyapunov equation method to determine whether the following system is asymptotically stable:
Dasi 1. For each of the following systems, determine whether the system is (1) stable, (2) causal, (3) linear, (4) time invariant, and (5) memoryless: (a) 7(x[n]) = g[n]X[n] with g[n] given (b) (x[n]) = x=no x[k] n20 (c) 7(x[n]) = (d) T(x[n]) = x[n - nol + x[k] (e) T(x[n]) = ex[n] (f) T(x[n]) = ax[n] + b (g) T(x[n]) = x[-n] (h) T(x[n]) = x[n] + 3u[n + 1).
For each of the following systems:
(i) Find the general solution by using eigenvalues and
eigenvectors.
(ii) State whether the origin is stable, asymptotically stable,
or unstable.
(iii) State whether the origin is a node, saddle, center, or
spiral.
For each of the following systems: (i) Find the general solution by using eigenvalues and eigenvectors. (ii) State whether the origin is stable, asymptotically stable, or unstable. |(iii) State whether the origin is a node, saddle, center, or spiral. Problem 1:...
#3 Find the fixed points and determine whether each ws Vottraiting (asymptotically stable) or a) S09243-** b) xxx c) *) 2 x?- repelling
#3 Find the fixed points and determine whether each Vattraiting (asymptotically stable) or repelling a) SX12 43-X b) xax =) (A) = *-*
3. Show tha the system of equations where r r2 + y2 has a limit cycle at r - To for each ro such that F(ro) = 0 and F,(m)メ0. The orbit is called asymptotically orbitally stable if F(ro) >0 and unstable if F(ro)0. For the case when F(r)r2)(2- 4r 3) find all limit cycles, determine the orbital stability, and sketch the orbits in the phase plane.
3. Show tha the system of equations where r r2 + y2 has...
2. (Chapter 2). A linear, time-invariant, continuous-time (LTIC) system with input f(t) and output y(t) is specified by the differential equation D2(D +1)y(t) (D - 3)f(t) Find the characteristic polynomial, characteristic equation, characteristic root(s), and characteristic mode(s) of this system. a. b. Is this system asymptotically stable, marginally stable, or unstable? Justify your answer.
2. (Chapter 2). A linear, time-invariant, continuous-time (LTIC) system with input f(t) and output y(t) is specified by the differential equation D2(D +1)y(t) (D - 3)f(t)...
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