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Doctoral Thesis
DOI
10.11606/T.18.2010.tde-08122010-145056
Document
Author
Full name
Amanda Liz Pacífico Manfrim
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2010
Supervisor
Committee
Terra, Marco Henrique (President)
Costa, Eduardo Fontoura
Costa, Oswaldo Luiz do Valle
Ishihara, João Yoshiyuki
Val, João Bosco Ribeiro do
Title in Portuguese
Sistemas lineares singulares sujeitos a saltos Markovianos
Keywords in Portuguese
Estabilidade de Lyapunov
Regulador linear quadrático
Regularidade
Sistemas singulares
Sistemas sujeitos a saltos Markovianos
Abstract in Portuguese
Esta tese trata das propriedades estruturais e do controle de sistemas lineares singulares sujeitos a saltos Markovianos (SLSSM). Três questões fundamentais são consideradas para esta classe de sistemas. A primeira estabelece condições necessárias para que o sistema seja estocasticamente regular em um período de tempo determinado. A segunda trata da estabilidade exponencial estocástica de SLSSM. Equações de Lyapunov acopladas generalizadas são deduzidas para caracterizar estabilidade deste tipo de sistema. Em virtude da complexidade das soluções numéricas dessas equações, cada equação de Lyapunov do conjunto acoplado está em função de duas variáveis desconhecidas, estamos propondo um algoritmo para resolver este problema. A terceira questão diz respeito à síntese de um regulador para este tipo de sistema singular definida em termos de equações algébricas generalizadas de Riccati acopladas.
Title in English
Singular linear systems subject to Markov jumps
Keywords in English
Linear quadract regulator
Lyapunov stability
Regularity
Singular systems
Systems with Markov jump parameters
Abstract in English
This thesis deals with the structural features and with the control of singular linear systems with Markovian jump parameters (SLSMJP). Three fundamental questions are considered to this class of systems. The first provides necessary conditions to characterize stochastic regularity in a determined period of time. The second deals with exponential stability of SLSMJP. Coupled generalized Lyapunov Equations are deduced to check the stability of this class of systems. In virtue of the complexity of the numerical solutions of these equations, there exist two unknown variables for each equation of the set of coupled Lyapunov equations, we are proposing an algorithm to solve this problem. The third question is related with the synthesis of a regulator for this class of singular systems defined in terms of coupled algebraic generalized Riccati equations.
 
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Amanda.pdf (1.04 Mbytes)
Publishing Date
2011-02-22
 
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