March 2019

28 mars 2019 – 14h, salle Europe

Speaker: Matteo Della Rossa
Title: Max-Min Lyapunov Functions for State-Dependent-Switched Systems
Keywords: Switched systems, Filippov regularization, Max-Min Lyapunov functions, set-valued derivatives, asymptotic stability.
Abstract: A class of locally Lipschitz continuous Lyapunov functions is studied in this talk to establish stability for differential inclusions obtained as the Filippov regularization of a non-continuous system arising from a switched systems with a state-dependent switching signal. Starting with a finite family of continuously differentiable positive definite functions, we study conditions under which a function obtained by max-min combinations over this family is a Lyapunov function. We investigate generalized notions of directional derivatives for these max-min of functions, and use them in deriving stability conditions with various degrees of conservatism, where the more conservative ones are numerically more tractable. The proposed constructions also provide nonconvex Lyapunov functions, which are shown to be useful for systems with state-dependent switching that do not admit a convex Lyapunov function.
Slides

Speaker: Ariadne Justi Bertolin (stage)
Title: LMI Conditions for Stability and Stabilization of Affine Uncertain Discrete-time Linear Systems
Keywords: Uncertainty, discrete-time systems, linear matrix inequalities, κ-stability
Abstract: This work investigates the stability and stabilizability of affine uncertain time-varying discrete-time systems by means of Linear Matrix Inequalities (LMIs) for arbitrary, limited and dynamic variations. As strategy, κ -1 redundant equations of the system is used to assure robust control and stability by sufficient LMIs conditions with distinct complexities. In this way, as κ≥1 increases, the conditions are progressively less conservatives. Numerical experiments, based on models borrowed from literature, will be performed, using computational tools available in Matlab to program the LMIs, together with parsers and solvers of public domain.

Speaker: Michelle Castro Ferreira De Faria (stage)
Title: Stabilization of uncertain discrete-time systems subject to a time-varying state-delay and input saturation constraints
Keywords: Discrete-time system, state-delay, input saturation
Abstract: In this talk, I will present a study on the stabilization of uncertain discrete time systems subject to a time-varying state-delay and input saturation constraints. These features are common in real processes and often cause undesired performance or even instability. The objectives are to establish synthesis conditions for a state feedback control law that guarantee the local asymptotic stability of the closed-loop system for a given set of initial conditions. We propose stability conditions obtained through two different approaches: a first method relies on Lyapunov-Krasovskii functionals while a second one is based on augmented systems formulation.