Search results for "Bounded function"
showing 10 items of 508 documents
Modelling of Systems with a Dispersed Phase: “Measuring” Small Sets in the Presence of Elliptic Operators
2016
When modelling systems with a dispersed phase involving elliptic operators, as is the case of the Stokes or Navier-Stokes problem or the heat equation in a bounded domain, the geometrical structure of the space occupied by the dispersed phase enters in the homogenization process through its capacity, a quantity which can be used to define the equivalence classes in \(H^1\). We shall review the relationship between capacity and homogenization terms in the limit when the number of inclusions becomes large, focusing in particular on the situation where the distribution of inclusions is not necessarily too regular (i.e. it is not periodic).
Bounded Palais–Smale sequences for non-differentiable functions
2011
The existence of bounded Palais-Smale sequences (briefly BPS) for functionals depending on a parameter belonging to a real interval and which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function, is obtained when the parameter runs in a full measure subset of the given interval. Specifically, for this class of non-smooth functions, we obtain BPS related to mountain pass and to global infima levels. This is done by developing a unifying approach, which applies to both cases and relies on a suitable deformation lemma. © 2011 Elsevier Ltd. All rights reserved.
Unbounded Linear Operators in Hilbert Spaces
2002
In order to make this monograph self-contained, we summarize in this chapter some basic definitions and results for unbounded linear operators in a Hilbert space. In Section 1.1, we recall the definitions of C*-algebras and von Neumann algebras. In Section 1.2, we define and investigate the notion of closedness, the closure and the adjoint of an unbounded linear operator in a Hilbert space. Section 1.3 is devoted to the Cayley transform approach to the self-adjointness of a symmetric operator. Section 1.4 deals with the self-adjoint extendability of a symmetric operator with help of the deficiency spaces. In Section 1.5, we extend to unbounded self-adjoint operators the spectral theorem and…
Nonlinear Analysis of Phase-Locked Loop (PLL): Global Stability Analysis, Hidden Oscillations and Simulation Problems
2013
In the middle of last century the problem of analyzing hidden oscillations arose in automatic control. In 1956 M. Kapranov considered a two-dimensional dynamical model of phase locked-loop (PLL) and investigated its qualitative behavior. In these investigations Kapranov assumed that oscillations in PLL systems can be self-excited oscillations only. However, in 1961, N. Gubar’ revealed a gap in Kapranov’s work and showed analytically the possibility of the existence of another type of oscillations, called later by the authors hidden oscillations, in a phase-locked loop model: from a computational point of view the system considered was globally stable (all the trajectories tend to equilibria…
Finite-Time Hâ Filtering for T-S Fuzzy Discrete-Time Systems with Time-Varying Delay and Norm-Bounded Uncertainties
2015
In this paper, we investigate the filtering problem of discrete-time Takagi–Sugeno (T–S) fuzzy uncertain systems subject to time-varying delays. A reduced-order filter is designed. With the augmentation technique, a filtering error system with delayed states is obtained. In order to deal with time delays in system states, the filtering error system is first transformed into two interconnected subsystems. By using a two-term approximation for the time-varying delay, sufficient delay-dependent conditions of finite-time boundedness and $H_{\infty }$ performance of the filtering error system are derived with the Lyapunov function. Based on these conditions, the filter design methods are propose…
Chaotic Scattering in the Gaussian Potential
1995
It is well known that general classical Hamiltonian dynamical systems have as a rule chaotic behaviour. By such a term one usually understands a sensitive dependence on initial conditions which manifests itself in the topology of phase space. For the most studied case of bounded motions this behaviour is detected, for example, by analysing the Poincare surfaces of section and by calculating Lyapunov characteristic exponents. The question then naturally arises of what are the effects of this complexity on the unbounded motions, i.e., on scattering phenomena. The signature of chaotic dynamics in these scattering regions of phase space has been the object of several papers appeared mainly in t…
Design of unknown inputs proportional integral observers for TS fuzzy models
2014
In this paper the design of unknown inputs proportional integral observers for Takagi-Sugeno (TS) fuzzy models subject to unmeasurable decision variables is proposed. These unknown inputs affect both state and output of the system. The synthesis of these observers is based on two hypotheses that the unknown inputs are under the polynomials form with their kth derivatives zero for the first one and bounded norm for the second one, hence two approaches. The Lyapunov theory and L"2-gain technique are used to develop the stability conditions of such observers in LMIs (linear matrix inequality) formulation. A simulation example is given to validate and compare the proposed design conditions for …
Adaptive neural state-feedback stabilizing controller for nonlinear systems with mismatched uncertainty
2014
In this paper, an adaptive neural network (NN) state-feedback controller for a class of nonlinear systems with mismatched uncertainties is presented. By using a radial basis (RBF) neural network, a bound of unknown nonlinear functions is approximated so that no information about the upper bound of mismatched uncertainties is required. The state-feedback is based on Lyapunov stability theory, and it is shown that the asymptotic convergence of the closed-loop system to zero is achieved while maintaining bounded states at the same time. The presented methods are more general than the previous approaches, handling systems with no restriction on the dimension of the system and the number of inpu…
Faults diagnosis based on proportional integral observer for TS fuzzy model with unmeasurable premise variable
2014
In this work, we focus on the synthesis of a Proportional Integral (PI) observer for the actuators and sensors faults diagnosis based on Takagi-Sugeno (TS) fuzzy model with unmeasurable premise variables. The faults estimation method is based on the assumption that these faults act as unknown inputs under polynomials form whose their kth derivatives are bounded. The convergence conditions of the observer as well as the faults reconstruction are established on the basis of the Lyapunov stability theory and the L 2 optimization technique, expressed as Linear Matrix Inequalities (LMI) constraints. In order to validate the proposed approach, a hydraulic system with two tanks is proposed.
From stationary state to endogenous growth: International trade in the mathematical formulation of the Ricardian system
2015
In his 1814–15 correspondence with Malthus and in his Essay on Profits, Ricardo championed the free importation of wage goods as a highly effective growth-enhancing policy. In order to capture this aspect in the mathematical formulation of the Ricardian system first introduced by Pasinetti in 1960 in the context of a closed economy, we produce a variant of that model where the economy is a small open one. We show that this economy is characterised by endogenous growth since the growth rate is bounded from below and we locate two thresholds concerning the allocation of labour among the two sectors of the economy and the pattern of international trade.