5. Consider the system in state variable form x = AX + Bu y = Cx + Du with A = [ ] B = [¹₁] C = [1 0], D = 0. Y(s) U(S) ii) Determine the system's controllability and observability. i) Determine the transfer function (s) =

Q: /5 -4 0) X' 1 0 2 2 5 ||

A: First find the Eigen value of the matrix:

Q: Find all equilibrium points for the following system of equations: x' = x-y+4 y'=3x-y+1

A:

Q: A system of the type i = f(x), f(x) = -gradV(x), is called a gradient system. Investigate the…

A: Given that, A system of the type x˙=fx, fx=-grad Vx is called a gradient system.  Investigate the…

Q: The nonlinear system A The corresponding linearized system at [a a_11 a_12 a_21 a_11 a_12 a_22 'x' =…

A:

Q: Consider the system x' - x = u(t). Can one steer 1 to 0 by a differentiable control function u(t)?…

A: Step 1:Consider the system x′−x=u(t)Can one steer 1 to 0 by a differentiable control function u(t) =…

Q: dx dt dy = −y − x(x² + y²)¹/2, = x − y(x² + y²)¹/2 dt (a) Show that the system is almost linear in…

A:

Q: 2. The behavior of the system is a saddle. x' = -x +y, y = -x-y

A: The given system of differential equations is:…

Q: 36 3 For the function of (x,, ^₂^3) = X₁ X² & ²₂², determme the gradient vector of first-order…

A:

Q: = 0. c) y(0) = 1, y'(0) = 0, y"(0) = -1. Is the set of functions linearly independent or linearly…

A:

Q: Use the elimination method to find a general solution for the given linear system, where…

A:

Q: 4) Demand for a model of SUV is given by the formula: √x D(x, y) = 45,000 10 (5y - 11)3/2 where x is…

A: Demand for a model of SUV is given by the formula, D(x,y)=45000-x2-10(5y-11)32 We have to find the…

Q: Find the number of equilibrium solutions of the r x' = x(y-2) โม่ = x − y

A: x'=x(y-2)y'=(x-y) Equilibrium solution of a system of differential equation X'=AX are those solution…

Q: Take the system Find a particular solution of the form *₁(t) = x₂ (t) = help (formulas) = v cos(4t)…

A:

Q: Find the solution to the given system that satisfies the given initial condition. x' (t) = (a) x(0)…

A:

Q: How do you remember the methods for partial derivatives in the chain rule for several variables?

A:

Q: Which of the following functions V(y1, Y2) is a Lyapunov function for the dynamical system y1 =…

A:

Q: 10.J Compute the matrix of partial derivatives of: f(x,y) = (x+y, x-y, xy) d.) f(x, y, z) =…

A:

Q: Assume that  dx1/dt= x1(2-x1)-x1x2 dx2/dt= x1x2-x2 a) Graph the zero isoclines. b) Show that (1,…

A:

Q: x' = 4x + y + 2t, y' = −2x + y

A:

Q: Linearize the system about each of the 4 equilibrium points and find the linear solutions y'…

A: For all four equilibrium points to be linearised of, we first need to find the equilibrium points…

Q: Find a particular solution of the linear system given. x'=3x-y y'=5x-3y where x(0) = 1, y(0) = -1

A: Given system of equation is., x' = 3x - yy' = 5x - 3y where x(0) = 1; y(0) = -1 First we find the…

Q: x' = x(3 − x+y) y = y(2+x-y), where x(0) ≥ 0, y(0) ≥ 0. Describe the global dynamics of the system

A: The given system of differential equations is: x'=x(3-x+y)  y'=y(2+14x−y),  Where x(0)≥0,y(0)≥0