Adaptive Control LMI-based design for descriptor systems rational in the uncertainties*

Uncertain systems are considered. They are represented in a descriptor form, where the matrices have an affine dependence on the uncertain parameter. S-variable approach for the design of a robust adaptive control feedback loop is presented. The only requirement to build such an adaptive law is robust stability of the closed-loop system by a static gain. No assumption about passivity of the system is made. Asymptotic stability of the given adaptive control is proved using Lyapunov arguments, and gain adaptation parameters are tunable by linear matrix inequality based convex optimization. An application to the attitude control of a microsatellite of the CNES Myriade series illustrates the results.