H∞ control of a flexible robotic arm (effect on parameter uncertainties on stability)

Describes the stability of a flexible robotic arm when its mathematical model contains parameter uncertainties. The authors employ the H_∞ control method which includes the LQ optimal control, and is robust. To estimate the stability domain of a closed-loop system, one must find the rate at which the system matrix A and the control matrix B change when a parameter changes. These rates are difficult to find, because the elements of the matrices change nonlinearly when the parameter changes. They calculate the rates approximately and obtain the stability domain by using the Routh condition. They also show some simulation results, demonstrating that the modeled stability domain of the one-degree-of-freedom flexible arm can be enlarged by appropriately choosing the arbitrary matrices of the H_∞ control law