Controllability, ∗-controllability and stabilizability

Asymptotic Controllability and Robust Asymptotic Stabilizability

This paper deals with asymptotically controllable systems for which there exists no smooth stabilizing state feedback. To investigate the robustness asymptotic stabilization property, a new class of hybrid feedbacks (with a continuous component and a discrete one) is introduced: the hybrid patchy feedbacks. The notion of solutions is a generalization of π-solutions and Euler solutions. It is pr...

Controllability and stabilizability of bimodal systems with discontinuous vector fields

Asymptotic controllability implies continuous-discrete time feedback stabilizability

In this paper, the relation between asymptotic controllability and feedback stabilizability of general nonlinear systems is investigated. It is proved that asymptotic controllability implies for any strictly positive sampling period of a stabilizing feedback in a continuous-discrete time framework. The proof uses receding horizon considerations to construct a stabilizing feedback.

The controllability of cardiac rhythm in elderly

Introduction: Recent reports have shown that rare fluctuations in cardiac cycles are ‘forgotten’ quickly in healthy individuals and it is possible to quantify the “memory length” of a physiological time-series using an inverse statistical approach. Methods: In the present study, we assessed the effect of aging on memory length in cardiac rhythm. Results: There was a long...

Consensus Stabilizability and Exact Consensus Controllability of Multi-agent Linear Systems

A goal in engineering systems is to try to control them. Control theory offers mathematical tools for steering engineered systems towards a desired state. Stabilizability and controllability can be studied under different points of view, in particular, we focus on measure of controllability in the sense of the minimum set of controls that need for to steer the multiagent system toward any desir...