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In this paper we show how to find convenient boundary actuators, termed boundary efficient actuators, ensuring finite-time space compensation of any boundary disturbance. This is the so-called remediability problem. Then we study the relationship between this remediability notion and controllability by boundary actuators, and hence the relationship between boundary strategic and boundary efficient actuators. We also determine the set of boundary remediable disturbances, and for a boundary disturbance,...
This special issue provides information on current and future research directions in the emerging field of Decentralized Control of Large Scale Complex Systems. There is generally adopted view that a dynamic system is large scale complex whenever it is necessary to partition its analysis or synthesis problem to manageable subproblems. Its fundamental characteristics in modeling and control are high dimensionality, uncertainty, information structure constraints, and delays. Theory of large scale...
We study in this paper Algebraic Riccati Equations associated with single-input single-output linear time-invariant systems bounded in -norm. Our study is focused in the characterization of families of Algebraic Riccati Equations in terms of strictly positive real (of zero relative degree) substitutions applied to the associated -norm bounded system, each substitution characterizing then a particular member of the family. We also consider here Algebraic Riccati Equations associated with systems...
In this work, we present some concepts recently introduced in the analysis and control of
distributed parameter systems: Spreadability,
vulnerability and protector control. These concepts
permit to describe many biogeographical phenomena, as those of pollution, desertification
or epidemics, which are characterized by a spatio-temporal evolution
The problem of boundary stabilization for the isotropic linear
elastodynamic system and the wave equation with Ventcel's
conditions are considered (see [12]). The boundary
observability and the exact controllability were etablished in [11]. We prove here the enegy decay to zero for the elastodynamic
system with stationary Ventcel's conditions by introducing a
nonlinear boundary feedback. We also give a boundary feedback
leading to arbitrarily large energy decay rates for the
elastodynamic system...
This paper focuses on the problem of constraint control for a class of discrete-time nonlinear systems. Firstly, a new discrete T-S fuzzy hyperbolic model is proposed to represent a class of discrete-time nonlinear systems. By means of the parallel distributed compensation (PDC) method, a novel asymptotic stabilizing control law with the “soft” constraint property is designed. The main advantage is that the proposed control method may achieve a small control amplitude. Secondly, for an uncertain...
In this paper we consider a linear system subject to norm bounded, bounded rate time-varying uncertainties. Necessary and sufficient conditions for quadratic stability and stabilizability of such class of uncertain systems are well known in the literature. Quadratic stability guarantees exponential stability in presence of arbitrary time-varying uncertainties; therefore it becomes a conservative approach when, as it is the case considered in this paper, the uncertainties are slowly-varying in time....
In order to better understand the dynamics of acute leukemia, and in particular to find
theoretical conditions for the efficient delivery of drugs in acute myeloblastic leukemia,
we investigate stability of a system modeling its cell dynamics. The overall system is a cascade connection of sub-systems consisting of distributed
delays and static nonlinear feedbacks. Earlier results on local asymptotic stability are
improved by the analysis of the linearized...
We introduce a model of a vibrating multidimensional structure made of a n-dimensional body and a one-dimensional rod. We actually consider the anisotropic elastodynamic system in the n-dimensional body and the Euler-Bernouilli beam in the one-dimensional rod. These equations are coupled via their boundaries. Using appropriate feedbacks on a part of the boundary we show the exponential decay of the energy of the system.
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