CONSTRUCTION OF COMPARISON SYSTEMS FOR ESTIMATION OF INTEGRAL FUNNELSIN DYNAMIC-SYSTEMS

Comparison systems are constructed for the estimation of integral funn els in dynamic systems. Two-sided guaranteeing bounds of the instantan eous time section of an integral funnel among sets bounded by level su rfaces of certain Lyapunov-like functions were obtained at any instant . The obtained comparison systems are used in various algorithms for e stimation of the studied sets. The problem of improving the constructe d estimates in the sense of the Lebesgue measure is formulated. Theore ms are proved that may significantly improve the obtained estimates. T he proposed methods can be extended to the estimation of reachable set s in control systems.