Erik I. Verriest

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This paper concerns an optimal control problem defined on a class of switched-mode hybrid dynamical systems. The system’s mode is changed (switched) whenever the state variable crosses a certain surface in the state space, henceforth called a switching surface. These switching surfaces are parameterized by finite-dimensional vectors called the switching(More)
The dynamics of hybrid systems with mode dynamics of different dimensions is described. The first part gives some deterministic examples of such multi-mode multi-dimensional (MD) systems. The second part considers such models under sequential switching at random times. More specifically, the backward Kolmogorov equation is derived, and Lie-algebraic methods(More)
A Lyapunov-type stability analysis for coupled delay differential and continuous time difference equations is given. Such systems are encountered as the internal dynamics of input output linearized nonlinear time delay systems. They appear also in lossless propagation models, in economics, in gas dynamics. The main contribution of this note is a two-step(More)
The optimal impulsive control problem for a system with a single discrete delay is studied. In such systems the control consists only of a sequence of modulated impulses, the control variables being the impulse times and their magnitudes. It is assumed that the systems considered all have a refractory period, in the sense that once an action is taken, it(More)
This paper introduces a new model for disease outbreaks. This model describes the disease evolution through a system of nonlinear differential equations with distributed-delay. The main difference between classical SIR-model resides in the fact that the recovery rate of the population is expressed as a distributed-delay term modeling the time spent being(More)