Singular linear systems subject to Markov jumps

Author(s)

Amanda Liz Pacífico Manfrim

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Escola de Engenharia de São Carlos (EESC/SBD)
• Defense date: 2010-10-08

Examining board members

Marco Henrique Terra; Eduardo Fontoura Costa; Oswaldo Luiz do Valle Costa; João Yoshiyuki Ishihara; João Bosco Ribeiro do Val

• Advisor: Marco Henrique Terra; Eduardo Fontoura Costa

Abstract

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. (AU)