Neste trabalho estudamos a estabilidade assintótica de Lagrange para duas classes de sistemas, sob as hipóteses de detetabilidade fraca e de limitação do custo medio a longo prazo. Para sistemas lineares com saltos markovianos com rudo aditivo, a equivalência entre estabilidade e as condições mencionadas sera provada. Para sistemas dinâmicos generalizados, provaremos a estabilidade sob uma condição adicional / In this work we study Lagrange asymptotic stability for two classes of systems, under conditions of weak detectability and boundedness of the long run average cost. For Markov jump linear systems with additive noise, the equivalence between stability and the aforementioned conditions is proved. For generalized dynamical systems, we prove stability under an additional condition

Neste trabalho estudamos a estabilidade assintótica de Lagrange para duas classes de sistemas, sob as hipóteses de detetabilidade fraca e de limitação do custo medio a longo prazo. Para sistemas lineares com saltos markovianos com rudo aditivo, a equivalência entre estabilidade e as condições mencionadas sera provada. Para sistemas dinâmicos generalizados, provaremos a estabilidade sob uma condição adicional / In this work we study Lagrange asymptotic stability for two classes of systems, under conditions of weak detectability and boundedness of the long run average cost. For Markov jump linear systems with additive noise, the equivalence between stability and the aforementioned conditions is proved. For generalized dynamical systems, we prove stability under an additional condition

<p>Traditional and cont emporary studies of spatial administrative systems are reviewed. Economic, political and historical factors are related to patterns of administrative areas. The hypothesized relationships are tested using data for the Ontario Hydro-Electric Power Commission. Linear and quadratic models relating functional costs to workload of the administrative areas are offered. The quadratic models incorporate the concept of the long-run average cost curve. A theoretical relationship between the shape of an administrative area and the level of economic efficiency is tested. Linear programming is used to simulate administrative patterns. Four indices are used to describe and compare the patterns. One of the indices, the weighted mean, is used to operationalise Pred's Behavioural Matrix . Recommendations are made for future work. </p> / Thesis / Doctor of Philosophy (PhD)