Imporved S-variable results applied to the analysis of time-varying uncertain systems
Résumé
Finite horizon performance analysis is addressed for time-varying uncertain linear systems. Results apply to state-space systems with matrices rational in both time and a scalar uncertainty. Performances include stability and L2 induced gain like criteria over a given time interval and extend to usual stability and L2 induced norm as the upper bound goes to infinity. Results are formalized in terms of linear matrix inequalities by applying the S-variable approach. Two improvements to this approach are proposed to reduce conservatism and deal with positive unbounded indeterminates such as time. Descriptor modeling is adopted and a lifting based methodology allows to build tractable results aiming at decreasing conservatism.