Optimal Control of Multirate Sampled-Data Systems

We have formulated a linear quadratic regulator design problem for slow input / fast output multirate sampled-data control systems. Discrete Maximum Principle is utilized to rigorously derive the periodic Riccati equation whose solution determines the feedback gain of the optimal multirate regulator. The Square Root Algorithm, on the other hand, is suggested as a tool to attain the numerical solution for the problem. Both approaches yield the same result, contrary to our initial thought.