On the design of linear systems with piecewise-constant feedback gains

This paper presents the theory and the computational algorithm required to determine the piecewise-constant feedback gains for the optimal control of a linear system with quadratic performance index over a finite control interval <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[t₀ T]</tex> . A third order example illustrates the relation of the piecewise-constant gains to the truly optimal time-varying gains.