An unstable robot system is described by the vector differential equation [9] Both state variables are measurable,

Question:

An unstable robot system is described by the vector differential equation [9]

Both state variables are measurable, and so the control signal is set as u(t) = -k(xi + x2). Following the method of Section 11.7, design gain k so that the performance index is minimized. Evaluate the minimum value of the performance index. Determine the sensitivity of the performance to a change in k. Assume that the initial conditions are