- ▪M. Marcondes de Freitas, E.D. Sontag, "A small-gain theorem for random dynamical systems with inputs and outputs", SIAM J. Control and Optimization, vol. 53, pp. 2657-2695, 2015. pdf
Abstract
A formalism for the study of random dynamical systems with inputs and outputs (RDSIO) is introduced. An axiomatic framework and basic properties of RDSIO are developed, and a theorem is shown that guarantees the stability of interconnected systems.
- ▪M. Skataric, E.D. Sontag, "Remarks on model-based estimation of nonhomogeneous Poisson processes and applications to biological systems", In Proc. European Control Conference, Strasbourg, France, June 2014, pp. 2052-2057, 2014. pdf
Abstract
This paper studies model-based estimation methods of a rate of a nonhomogeneous Poisson processes that describes events arising from modeling biological phenomena in which discrete events are measured. We describe an approach based on observers and Kalman filters as well as preliminary simulation results, and compare these to other methods (not model-based) in the literature. The problem is motivated by the question of identification of internal states from neural spikes and bacterial tumbling behavior.
- ▪M. Marcondes de Freitas, E.D. Sontag, "Random dynamical systems with inputs", In Nonautonomous Dynamical Systems in the Life Sciences, Lecture Notes in Mathematics vol.\ 2102, pp. 41-87, 2013. pdf
Abstract
This work introduces a notion of random dynamical systems with inputs, providing several basic definitions and results on equilibria and convergence. It also presents a "converging input to converging state" result, a concept that plays a key role in the analysis of stability of feedback interconnections, for monotone systems.
- ▪M. Marcondes de Freitas, E.D. Sontag, "A class of random control systems: Monotonicity and the convergent-input convergent-state property", In Proc. American Control Conference, pp. 4564-4569, 2013. pdf