57,309 research outputs found
Uniform Stability Analysis for Time-Varying Systems Applying Homogeneity
International audienceThe uniform stability notion for a class of non-linear time-varying systems is studied using the homogeneity framework. It is assumed that the system is weighted homogeneous considering the time variable as a constant parameter, then several conditions of uniform stability for such a class of systems are formulated. The results are applied to the problem of adaptive estimation for a linear system
Continuous Uniform Finite Time Stabilization of Planar Controllable Systems
Continuous homogeneous controllers are utilized in a full state feedback setting for the uniform finite time stabilization of a perturbed double integrator in the presence of uniformly decaying piecewise continuous disturbances. Semiglobal strong Lyapunov functions are identified to establish uniform asymptotic stability of the closed-loop planar system. Uniform finite time stability is then proved by extending the homogeneity principle of discontinuous systems to the continuous case with uniformly decaying piecewise continuous nonhomogeneous disturbances. A finite upper bound on the settling time is also computed. The results extend the existing literature on homogeneity and finite time stability by both presenting uniform finite time stabilization and dealing with a broader class of nonhomogeneous disturbances for planar controllable systems while also proposing a new class of homogeneous continuous controllers
Uniform stabilization for linear systems with persistency of excitation. The neutrally stable and the double integrator cases
Consider the controlled system where the pair
is stabilizable and takes values in and is
persistently exciting, i.e., there exist two positive constants such
that, for every , . In particular,
when becomes zero the system dynamics switches to an uncontrollable
system. In this paper, we address the following question: is it possible to
find a linear time-invariant state-feedback , with only depending on
and possibly on , which globally asymptotically stabilizes the
system? We give a positive answer to this question for two cases: when is
neutrally stable and when the system is the double integrator
On the stabilization of persistently excited linear systems
We consider control systems of the type , where
, is a controllable pair and is an unknown
time-varying signal with values in satisfying a persistent excitation
condition i.e., \int_t^{t+T}\al(s)ds\geq \mu for every , with
independent on . We prove that such a system is stabilizable
with a linear feedback depending only on the pair if the eigenvalues
of have non-positive real part. We also show that stabilizability does not
hold for arbitrary matrices . Moreover, the question of whether the system
can be stabilized or not with an arbitrarily large rate of convergence gives
rise to a bifurcation phenomenon in dependence of the parameter
Robust exact differentiators with predefined convergence time
The problem of exactly differentiating a signal with bounded second
derivative is considered. A class of differentiators is proposed, which
converge to the derivative of such a signal within a fixed, i.e., a finite and
uniformly bounded convergence time. A tuning procedure is derived that allows
to assign an arbitrary, predefined upper bound for this convergence time. It is
furthermore shown that this bound can be made arbitrarily tight by appropriate
tuning. The usefulness of the procedure is demonstrated by applying it to the
well-known uniform robust exact differentiator, which the considered class of
differentiators includes as a special case
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