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44. Determine the stability of the origin for the system, S x'(t) = –23 + 2.25...
Problem 9. Consider the discrete time dynamical system (a) Determine stability of the origin. (b)...
Problem 9. Consider the discrete time dynamical system (a) Determine stability of the origin. (b) Describe dynamics of the system. (c) Sketch the phase portrait. y(k + 1)「L 3y(A)-42(k)
Problem 9. Consider the discrete time dynamical system (a) Determine stability of the origin. (b) Describe dynamics of the system. (c) Sketch the phase portrait. y(k + 1)「L 3y(A)-42(k)
7. Consider the system 1 2 y (a) Show that the origin is a fixed point, and determine its stability (b) Show that the origin is the only fixed point. Hint: Argue using a theorem or result based on pr...
7. Consider the system 1 2 y (a) Show that the origin is a fixed point, and determine its stability (b) Show that the origin is the only fixed point. Hint: Argue using a theorem or result based on properties of the matrix.
7. Consider the system 1 2 y (a) Show that the origin is a fixed point, and determine its stability (b) Show that the origin is the only fixed point. Hint: Argue using a theorem or result...
For LTI dynamical system (0 y(t) 1 0(t) study the internal stability, the controllability and the...
For LTI dynamical system (0 y(t) 1 0(t) study the internal stability, the controllability and the observability of the system; before computing G(s), try to figure out the BIBO stability properties of the system given the information obtained at the previous point; compute G(s), verifying that, if the system is not fully controllable or not fully observable, some zero/pole cancellations occur; also, draw conclusions about BIBO stability.
For LTI dynamical system (0 y(t) 1 0(t) study the internal stability, the...
Problem 1 Y(s) Given G(s) H(s) 0(s)-1 a) Determine the transfer function T(s) of the system above. b) Determine the mamber of RHP or L.HP poles of the system. Is tdhe system stable? Why or why no?...
Problem 1 Y(s) Given G(s) H(s) 0(s)-1 a) Determine the transfer function T(s) of the system above. b) Determine the mamber of RHP or L.HP poles of the system. Is tdhe system stable? Why or why no? c) H HG) were modified as follows. Determine the system stability as a function of parameter k, i.e, what is the minimal value of k required to keep the system stable? d) Sketch Bode the plot for T(s) including data 'k, derived from...
Problem #3 Use Routh's stability criterion to determine the stability of the following system. Also, determine...
Problem #3 Use Routh's stability criterion to determine the stability of the following system. Also, determine the number of poles in the LHP, RHP, and on the ju-axis T(s) -
At t = 0 s, a particle starts from the origin of a coordinate system and...
At t = 0 s, a particle starts from the origin of a coordinate system and moves in the xy plane with a velocity ~v = (7.9ˆi − 3.2ˆj) m/s. Determine the x position of the particle at t = 2.0 s.
External Stability Problem Determine the following systems are BIBO stable? (a) y(t)-x(t) *x(t) (b) y(t)=tx(t) (c)...
External Stability Problem
Determine the following systems are BIBO stable? (a) y(t)-x(t) *x(t) (b) y(t)=tx(t) (c) y(t)-d(/d
Assignment 1-2019 1. X: 23 22 44 12 25  
Assignment 1-2019 1. X: 23 22 44 12 25 24 16 50 42 21 21 36 23 22 41 Y: 50 50 50 50 50 49 43 44 48 47 46 8 3 4 2 P: 5 3 5 7 12 5 43 15 17 11 48 50 41 12 50 a) Make a frequency distributions for data set x and i=1 b) Combine set x, y and p and make a grouped frequency distribution (use i = 4, first bin 2-5). c) Using the same data and distribution add a column that shows the proportion frequency and the relative frequency (%) d) add a further column that shows the cumulative frequency. 2. Use the following grouped frequency distribution to answer the following questions. Score f...
5. Determine the possible equilibrium states of the system and investigate their stability by the first...
5. Determine the possible equilibrium states of the system and investigate their stability by the first method of Lyapunov, if it is described by a system of AN = P(x, y); 7 = Q(x, y) equations p dt P(x, y) = 2x²y +1 Q(x, y) = x + y
Consider the nonlinear system: - x + (x – 1) y y + 4x° (1 –...
Consider the nonlinear system: - x + (x – 1) y y + 4x° (1 – x). (a) Show that the system has a unique fixed point at the origin (0, 0). (b) Use a linear approximation to determine the stability of the fixed point. (c) Apply the Liapunov direct method to determine the stability of the fixed point. Is your conclusion different form that of Part (a)? Why? (d) Can the system have closed orbits (trajectories)? Explain.
Problem 9. Consider the discrete time dynamical system (a) Determine stability of the origin. (b) Describe dynamics of the system. (c) Sketch the phase portrait. y(k + 1)「L 3y(A)-42(k)
Problem 9. Consider the discrete time dynamical system (a) Determine stability of the origin. (b) Describe dynamics of the system. (c) Sketch the phase portrait. y(k + 1)「L 3y(A)-42(k)
7. Consider the system 1 2 y (a) Show that the origin is a fixed point, and determine its stability (b) Show that the origin is the only fixed point. Hint: Argue using a theorem or result based on properties of the matrix.
7. Consider the system 1 2 y (a) Show that the origin is a fixed point, and determine its stability (b) Show that the origin is the only fixed point. Hint: Argue using a theorem or result...
For LTI dynamical system (0 y(t) 1 0(t) study the internal stability, the controllability and the observability of the system; before computing G(s), try to figure out the BIBO stability properties of the system given the information obtained at the previous point; compute G(s), verifying that, if the system is not fully controllable or not fully observable, some zero/pole cancellations occur; also, draw conclusions about BIBO stability.
For LTI dynamical system (0 y(t) 1 0(t) study the internal stability, the...
Problem 1 Y(s) Given G(s) H(s) 0(s)-1 a) Determine the transfer function T(s) of the system above. b) Determine the mamber of RHP or L.HP poles of the system. Is tdhe system stable? Why or why no? c) H HG) were modified as follows. Determine the system stability as a function of parameter k, i.e, what is the minimal value of k required to keep the system stable? d) Sketch Bode the plot for T(s) including data 'k, derived from...
Problem #3 Use Routh's stability criterion to determine the stability of the following system. Also, determine the number of poles in the LHP, RHP, and on the ju-axis T(s) -
External Stability Problem
Determine the following systems are BIBO stable? (a) y(t)-x(t) *x(t) (b) y(t)=tx(t) (c) y(t)-d(/d
5. Determine the possible equilibrium states of the system and investigate their stability by the first method of Lyapunov, if it is described by a system of AN = P(x, y); 7 = Q(x, y) equations p dt P(x, y) = 2x²y +1 Q(x, y) = x + y
Consider the nonlinear system: - x + (x – 1) y y + 4x° (1 – x). (a) Show that the system has a unique fixed point at the origin (0, 0). (b) Use a linear approximation to determine the stability of the fixed point. (c) Apply the Liapunov direct method to determine the stability of the fixed point. Is your conclusion different form that of Part (a)? Why? (d) Can the system have closed orbits (trajectories)? Explain.
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