Banca de QUALIFICAÇÃO: LUÍS FELIPE VIEIRA SILVA

Uma banca de QUALIFICAÇÃO de DOUTORADO foi cadastrada pelo programa.
STUDENT : LUÍS FELIPE VIEIRA SILVA
DATE: 26/07/2025
TIME: 14:00
LOCAL: Remoto
TITLE:

Stability Analysis of the 0D Cardiovascular System Model as a Periodic Switched System via a Lyapunov Function with Continuous and Time-Varying Matrix Polynomials

KEY WORDS:

Switched Systems, Lyapunov Stability, Cardiovascular Modeling, Left Ventricular Assist Device (LVAD), Time-Varying Systems, Linear Matrix Inequalities (LMI), Hybrid Systems.

PAGES: 80
BIG AREA: Engenharias
AREA: Engenharia Elétrica
SUMMARY:

The stability analysis of mathematical models of the cardiovascular system (CVS) is fundamental to understanding the transition between healthy and pathological states. This challenge is intensified by the presence of Left Ventricular Assist Devices (LVADs), which introduce additional dynamics. This work presents a rigorous stability analysis of a lumped-parameter (0D) model of the CVS-LVAD system. The main hypothesis is that this system can be formalized as a linear time-varying (LTV) switched dynamical system, where the operating modes correspond to the four phases of the cardiac cycle, and the LTV dynamics are dictated by the heart's elastance function. Due to the inadequacy of conventional stability methods for this class of systems, an methodology based on Lyapunov functions with continuous time-varying matrix polynomials was adopted. The model was computationally implemented, and the state-space matrices for each mode were identified. The stability conditions, formulated as a set of Linear Matrix Inequalities (LMIs), were solved using convex optimization tools. This dissertation points to the analysis of a complex and clinically relevant hybrid system, establishing a mathematical framework for future investigations into the interaction between assist devices and cardiovascular physiology.

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