Dynamical analysis of complex systems in light of H-matrices

Predmet istraživanja ove doktorske disertacije je sistematsko povezivanje dinamičkih svojstava kompleksnih sistema (kao što su stabilnost, robusnost, reaktivnost, tranziciono ponašanje, amplifikacioni okvir) sa teorijom H-matrica, koje je motivisalo nove rezultate iz oblasti lokalizacije blok i frakcionog pseudospektra, kao i ocene norme inverzne matrice, kako u tačkastoj, tako i u blok formi, ali i primenu ovih rezultata u dinamičkoj analizi kompleksnih sistema.This thesis provides a systematic link between the dynamical properties of complex systems (such as  stability, robustness, reactivity, transient behavior, amplification envelope) and the theory of H-matrices, which has motivated new results as far as block and fractional pseudospectrum localizations are concerned, as well as some new upper bounds for the inverse of certain subclasses of H-matrices, both in the point-wise and block case, and the overall collective application of these results in the dynamical analysis of complex systems