Complex Nonsymmetric Algebraic Riccati Equations And Its Applications In Stochastic Fluid Flow Models

In this thesis, we study a new class of complex nonsymmetric algebraic Riccati equation arising in Markov Modulated Fluid Flows. We prove there exists a unique extremal solution for this new class, and design some of iterative methods to deliver the extremal solution. Combined with its dual equation, we give the decomposition of the key matrix, by which we study the transient analysis of the stochastic fluid flow models in perspective of matrix theory, the result coincides with the one obtained by probabilistic argument. However, our formulae are simpler and easier to compute.