Mathematical Sciences: Discrete Time Control

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This project concerns the theory of discrete deterministic nonlinear control systems and their relationship to continuous time models. The interest is both discrete time results as such and on sampling and other discretization techniques, with an emphasis on certain subclasses such as invertible, polynomial and piecewise linear systems. The theory builds on past research by the PI and others in these areas. For invertible systems, it is now possible to obtain Lie-algebraic accessibility conditions very analogous to those known for continuous time systems. In polynomial case, elementary techniques from algebraic geometry become useful. Regarding sampling, the main objective is the understanding of how properties of continuous time physical systems are preserved under digital control.