20 research outputs found
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Filtering for nonlinear genetic regulatory networks with stochastic disturbances
In this paper, the filtering problem is investigated for nonlinear genetic regulatory networks with stochastic disturbances and time delays, where the nonlinear function describing the feedback regulation is assumed to satisfy the sector condition, the stochastic perturbation is in the form of a scalar Brownian motion, and the time delays exist in both the translation process and the feedback regulation process. The purpose of the addressed filtering problem is to estimate the true concentrations of the mRNA and protein. Specifically, we are interested in designing a linear filter such that, in the presence of time delays, stochastic disturbances as well as sector nonlinearities, the filtering dynamics of state estimation for the stochastic genetic regulatory network is exponentially mean square stable with a prescribed decay rate lower bound beta. By using the linear matrix inequality (LMI) technique, sufficient conditions are first derived for ensuring the desired filtering performance for the gene regulatory model, and the filter gain is then characterized in terms of the solution to an LMI, which can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures
On Resilient Control of Nonlinear Systems under Denial-of-Service
We analyze and design a control strategy for nonlinear systems under
Denial-of-Service attacks. Based on an ISS-Lyapunov function analysis, we
provide a characterization of the maximal percentage of time during which
feedback information can be lost without resulting in the instability of the
system. Motivated by the presence of a digital channel we consider event-based
controllers for which a minimal inter-sampling time is explicitly
characterized.Comment: 7 pages, 1 figur
A graph theoretic approach to input-to-state stability of switched systems
This article deals with input-to-state stability (ISS) of discrete-time
switched systems. Given a family of nonlinear systems with exogenous inputs, we
present a class of switching signals under which the resulting switched system
is ISS. We allow non-ISS systems in the family and our analysis involves
graph-theoretic arguments. A weighted digraph is associated to the switched
system, and a switching signal is expressed as an infinite walk on this
digraph, both in a natural way. Our class of stabilizing switching signals
(infinite walks) is periodic in nature and affords simple algorithmic
construction.Comment: 14 pages, 1 figur
Two characterizations of switched nonlinear systems with average dwell time
This note aims to establish the fast switching condition with average dwell time satisfying an upper bound. Important results are obtained on the behaviour of switched nonlinear dynamical systems. In specific, this note contributes in the following three aspects: (1) establish the condition of fast switching of switched nonlinear systems; (2) obtain the condition of arbitrary switching stability of switched nonlinear dynamical systems using a weak Lyapunov functions approach; and (3) prove the necessity of the average dwell time condition associated with the conventional multiple Lyapunov functions’ framework
Stabilizing switching signals: a transition from point-wise to asymptotic conditions
Characterization of classes of switching signals that ensure stability of
switched systems occupies a significant portion of the switched systems
literature. This article collects a multitude of stabilizing switching signals
under an umbrella framework. We achieve this in two steps: Firstly, given a
family of systems, possibly containing unstable dynamics, we propose a new and
general class of stabilizing switching signals. Secondly, we demonstrate that
prior results based on both point-wise and asymptotic characterizations follow
our result. This is the first attempt in the switched systems literature where
these switching signals are unified under one banner.Comment: 7 page
Towards ISS disturbance attenuation for randomly switched systems
We are concerned with input-to-state stability (ISS) of randomly switched
systems. We provide preliminary results dealing with sufficient conditions for
stochastic versions of ISS for randomly switched systems without control
inputs, and with the aid of universal formulae we design controllers for
ISS-disturbance attenuation when control inputs are present. Two types of
switching signals are considered: the first is characterized by a statistically
slow-switching condition, and the second by a class of semi-Markov processes.Comment: 6 pages, to appear in the Proceedings of the 46th IEEE Conference on
Decision & Control, 200