A general solution to the stepsize scaling problem in sequential algorithms for computing optimal static output feedback gains

This paper solves the long-standing stepsize scaling problem that exists in the sequential algorithms for computing linear quadratic optimal static output feedback gains. We first review the linear quadratic optimal static output feedback problem. Then we discuss and briefly derive a sequential algorithm. After that we show how the stepsize scaling problem would naturally arise. We derive the exact upper bound for the scaling and explain why, as reported in the literature, the sequential algorithms may fail to give solutions. Following that, we give a general solution to the scaling problem that guarantees closed loop asymptotic stability. The new scaling method is applicable to first order and second order algorithms. The proposed solution is much more efficient compared to the existing method, as the latter involves repeated computation of closed loop eigenvalues or verification of matrix positive definiteness condition, that is computationally much more expensive.