818 research outputs found
Homogeneity in the bi-limit as a tool for observer and feedback design
International audienceWe introduce an extension of the notion of homogeneous approximation to make it valid both at the origin and at infinity (homogeneity in the bi-limit). Exploiting this extension, we give several results concerning stability, robustness and uniform (in the initial condition) finite time convergence for a homogeneous in the bi-limit vector field. We then introduce a homogeneous in the bi-limit observer and state-feedback for a chain of integrators. Combining these two tools we establish a global asymptotic stabilization result by output feedback for feedback and feedforward systems. We obtain also a finite time observer for globally Lipschitz system
Homogeneous Approximation, Recursive Observer Design, and Output Feedback
We introduce two new tools that can be useful in nonlinear observer and
output feedback design. The first one is a simple extension of the notion of
homogeneous approximation to make it valid both at the origin and at infinity
(homogeneity in the bi-limit). Exploiting this extension, we give several
results concerning stability and robustness for a homogeneous in the bi-limit
vector field. The second tool is a new recursive observer design procedure for
a chain of integrator. Combining these two tools, we propose a new global
asymptotic stabilization result by output feedback for feedback and feedforward
systems
Finite-time stabilization of homogeneous non-Lipschitz systems
This paper focuses on the problem of finite-time stabilization of homogeneous, non-Lipschitz systems with dilations. A key contribution of this paper is the design of a virtual recursive Holder, non-Lipschitz state feedback, which renders the non-Lipschitz systems in the
special case dominated by a lower-triangular nonlinear system finite-time stable. The proof is based
on a recursive design algorithm developed recently to construct the virtual Holder continuous, finite-time stabilizer as well as a C1 positive definite and proper Lyapunov function that guarantees finite-time stability of the non-Lipschitz nonlinear systems
Finite-time and fixed-time stabilization for integrator chain of arbitrary order
International audienceIn the present paper, homogeneous control laws are designed for finite-time and fixed-time stabilization of integrator chains of arbitrary order. Provided analysis is based on Lyapunov function method and homogeneity concept. Fixed-time convergence is achieved by use of hybrid control algorithm with homogeneity degree changing. Performance of the resulting finite-time and fixed-time feedbacks is illustrated by numerical simulations
Scale-free Linear Observer-based Protocol Design for Global Regulated State Synchronization of Homogeneous Multi-agent Systems with Non-introspective Agents Subject to Input Saturation
This paper studies global regulated state synchronization of homogeneous
networks of non-introspective agents in presence of input saturation. We
identify three classes of agent models which are neutrally stable,
double-integrator, and mixed of double-integrator, single-integrator and
neutrally stable dynamics. A \textit{scale-free linear observer-based} protocol
design methodology is developed based on localized information exchange among
neighbors where the reference trajectory is given by a so-called exosystem
which is assumed to be globally reachable. Our protocols do not need any
knowledge about the communication network topology and the spectrum of
associated Laplacian matrix. Moreover, the proposed protocol is scalable and is
designed based on only knowledge of agent models and achieves synchronization
for any communication graph with arbitrary number of agents.Comment: arXiv admin note: text overlap with arXiv:2004.09498,
arXiv:1908.06535, arXiv:2001.02117, arXiv:2002.0657
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