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

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

Is the system stable without the feedback signals due to u(0?

0 1 x(0)

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