484 research outputs found
Singularly Perturbed Stochastic Hybrid Systems: Stability and Recurrence via Composite Nonsmooth Foster Functions
We introduce new sufficient conditions for verifying stability and recurrence
properties in singularly perturbed stochastic hybrid dynamical systems.
Specifically, we focus on hybrid systems with deterministic continuous-time
dynamics that exhibit multiple time scales and are modeled by constrained
differential inclusions, as well as discrete-time dynamics modeled by
constrained difference inclusions with random inputs. By assuming regularity
and causality of the dynamics and their solutions, respectively, we propose a
suitable class of composite nonsmooth Lagrange-Foster and Lyapunov-Foster
functions that can certify stability and recurrence using simpler functions
related to the slow and fast dynamics of the system. We establish the stability
properties with respect to compact sets, while the recurrence properties are
studied only for open sets
Dynamics of Structured Systems
[no abstract available
Hybrid Bifurcations and Stable Periodic Coexistence for Competing Predators
We describe a new mechanism that triggers periodic orbits in smooth dynamical
systems. To this end, we introduce the concept of hybrid bifurcations: Such
bifurcations occur when a line of equilibria with an exchange point of normal
stability vanishes. Our main result is the existence and stability criteria of
periodic orbits that bifurcate from breaking a line of equilibria. As an
application, we obtain stable periodic coexistent solutions in an ecosystem for
two competing predators with Holling's type II functional response
Estimation and control of non-linear and hybrid systems with applications to air-to-air guidance
Issued as Progress report, and Final report, Project no. E-21-67
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