Invariant polytopes of linear systems

Stable linear systems possess invariant sets which have hyperellipsoidalregions associated with their Lyapunov function. In real systems,however, state and control variables are often confined in boundedpolyhedral regions(polytopes) so that a set of linear inequalitieshas to be satisfied. In this paper, necessary and sufficientconditions for the existence of positively invariant polytopesfor both discrete-time and continuous-time linear systems aregiven in terms of their spectral properties.     

Thermal and Mechanical Properties of Isotactic Polypropylene/TiO_2 Particulate Composites

It has been recently demonstrated that titanium dioxide possesses photocatalyticaction in the decomposition of ethylene to carbon dioxide and water in the presence ofatmospheric oxygen[1～ 3] . Ti O2 ,a largely produced substance exploited in manyindustrial sectors,is used as an additive in cosmetics and even in some food,because ofits very low toxicity level. Furthermore,Ti O2 shows absorption properties that canavoid water condensation on the interior surface of packages in the presence of …