37,066 research outputs found
Revisiting the Complexity of Stability of Continuous and Hybrid Systems
We develop a framework to give upper bounds on the "practical" computational
complexity of stability problems for a wide range of nonlinear continuous and
hybrid systems. To do so, we describe stability properties of dynamical systems
using first-order formulas over the real numbers, and reduce stability problems
to the delta-decision problems of these formulas. The framework allows us to
obtain a precise characterization of the complexity of different notions of
stability for nonlinear continuous and hybrid systems. We prove that bounded
versions of the stability problems are generally decidable, and give upper
bounds on their complexity. The unbounded versions are generally undecidable,
for which we give upper bounds on their degrees of unsolvability
A dynamical system analysis of hybrid metric-Palatini cosmologies
The so called hybrid metric-Palatini gravity presents a unique viable
generalisation of the theories within the metric-affine formalism. Here
the cosmology of the theories is studied using the dynamical system
approach. The method consists of formulating the propagation equation in terms
of suitable (expansion-normalised) variables as an autonomous system. The fixed
points of the system then represent exact cosmological solutions described by
power-law or de Sitter expansion. The formalism is applied to two classes of
models, revealing both standard cosmological fixed points and new
accelerating solutions that can be attractors in the phase space. In addition,
the fixed point with vanishing expansion rate are considered with special care
in order to characterise the stability of Einstein static spaces and bouncing
solutions.Comment: 13 page
Reset control for DC-DC converters: an experimental application
© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Power converters in grid connected systems are required to have fast response to ensure the stability of the system. The standard PI controllers used in most power converters are capable of fast response but with significant overshoot. In this paper a hybrid control technique for power converter using a reset PI + CI controller is proposed. The PI + CI controller can overcome the limitation of its linear counterpart (PI) and ensure a fast flat response for power converter. The design, stability and cost of feedback analysis for a DC-DC boost converter employing a PI + CI controller is explored in this work. The simulation and experimental results which confirm the fast, flat response will be presented and discussed.Peer ReviewedPostprint (published version
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