Improved S-variable results applied to the analysis of time-varying uncertain systems

Finite-horizon performance analysis is addressed for time-varying uncertain linear systems. The results apply to state-space models with matrices rational in both time and a scalar uncertainty. Performance measures include finite-time stability and L 2 induced gain like criteria, which converge to standard stability and L 2 induced norm as the time horizon 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. A descriptor modeling framework and a lifting-based methodology are used to build tractable results aiming at decreasing conservatism.