On design of multi-rate sampled-data output feedback by maximizing RSR

This paper investigates Multirate sampled-data control system optimization design by considering robust stability of linear time-invariant uncertain systems described by affine parameter-dependent model. Extend Lyapunov upper bound robust stability test to develop a new condition for robust stability test of such system and give out a reliable numerical algorithm. For a given compensator F, define the maximum uncertainty set radius that the system is stable with as RSR (robust stability radius). Then convert the RSR calculation problem to a mathematical process of solving an equation by analyzing the robust stability test condition proposed. Solve the equation with Numerical Mathematical methods and get the analytical solution as RSR. At last we can define the RSR as a function of F and achieve F optimization design by a general optimization method to get the biggest RSR. With this F, the system can remain stable with the uncertain parameters vary set being the largest.