8,963 research outputs found
Constructions of Strict Lyapunov Functions for Discrete Time and Hybrid Time-Varying Systems
We provide explicit closed form expressions for strict Lyapunov functions for
time-varying discrete time systems. Our Lyapunov functions are expressed in
terms of known nonstrict Lyapunov functions for the dynamics and finite sums of
persistency of excitation parameters. This provides a discrete time analog of
our previous continuous time Lyapunov function constructions. We also construct
explicit strict Lyapunov functions for systems satisfying nonstrict discrete
time analogs of the conditions from Matrosov's Theorem. We use our methods to
build strict Lyapunov functions for time-varying hybrid systems that contain
mixtures of continuous and discrete time evolutions.Comment: 14 pages. Accepted for publication in Nonlinear Analysis: Hybrid
Systems and Applications on September 6, 200
Robust Stability Analysis of Nonlinear Hybrid Systems
We present a methodology for robust stability analysis of nonlinear hybrid systems, through the algorithmic construction of polynomial and piecewise polynomial Lyapunov-like functions using convex optimization and in particular the sum of squares decomposition of multivariate polynomials. Several improvements compared to previous approaches are discussed, such as treating in a unified way polynomial switching surfaces and robust stability analysis for nonlinear hybrid systems
Input to State Stability of Bipedal Walking Robots: Application to DURUS
Bipedal robots are a prime example of systems which exhibit highly nonlinear
dynamics, underactuation, and undergo complex dissipative impacts. This paper
discusses methods used to overcome a wide variety of uncertainties, with the
end result being stable bipedal walking. The principal contribution of this
paper is to establish sufficiency conditions for yielding input to state stable
(ISS) hybrid periodic orbits, i.e., stable walking gaits under model-based and
phase-based uncertainties. In particular, it will be shown formally that
exponential input to state stabilization (e-ISS) of the continuous dynamics,
and hybrid invariance conditions are enough to realize stable walking in the
23-DOF bipedal robot DURUS. This main result will be supported through
successful and sustained walking of the bipedal robot DURUS in a laboratory
environment.Comment: 16 pages, 10 figure
Mathematical control of complex systems
Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
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
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