Search results for "linear"
showing 10 items of 7165 documents
Robust H<inf>&#x221E;</inf> control of Markovian jump systems with mixed time delays
2010
In this paper, the problem of stability analysis and control synthesis for Markovian jump linear systems with time delays and norm-bounded uncertainties is studied. The model under consideration consists of different time-invariant discrete, neutral and distributed delays. Delay-dependent sufficient conditions for the design of a mode-dependent delayed state feedback H ∞ control are given in terms of linear matrix inequalities (LMIs). A controller which guarantees stochastic stability and a prescribed level of H ∞ performance for the closed-loop system is then developed. A Lyapunov-Krasovskii functional (LKF) method underlies the control design. A numerical example with simulation results i…
Non-Stationary Probabilistic Response of Linear Systems Under Non-Gaussian Input
1991
The probabilistic characterization of the response of linear systems subjected to non-normal input requires the evaluation of higher order moments than two. In order to obtain the equations governing these moments, in this paper the extension of the Ito’s differential rule for linear systems excited by non-normal delta correlated processes is presented. As an application the case of the delta correlated compound Poisson input process is treated.
A New Family of Deformations of Darboux-Pöschl-Teller Potentials
2004
The aim of this Letter is to present a new family of integrable functional-difference deformations of the Schrodinger equation with Darboux–Poschl–Teller potentials. The related potentials are labeled by two integers m and n, and also depend on a deformation parameter h. When h→ 0 the classical Darboux–Poschl–Teller model is recovered.
High Resolution Coherent Raman Spectroscopy: Studies of Molecular Structures
1992
One of the main advantages of the non-linear coherent Raman techniques is the high resolution that can be achieved in rovibrational spectroscopy. Typically an instrumental function of the order of several thousandths of a wavenumber is routinely achieved in SRS or CARS experiments. Since the first recording of the stimulated Raman spectrum of 12CH4 in 1978 [1], numerous studies of molecules have been performed [2–8]. We have built a stimulated Raman experiment in Dijon in which particular attention has been paid to the frequency measurement of the Raman lines [9]. We will describe the application of our experiment to a wide variety of molecules over the last few years: linear molecules, sph…
Non Linear Systems Under Complex α-Stable Le´vy White Noise
2003
The problem of predicting the response of linear and nonlinear systems under Levy white noises is examined. A method of analysis is proposed based on the observation that these processes have impulsive character, so that the methods already used for Poisson white noise or normal white noise may be also recast for Levy white noises. Since both the input and output processes have no moments of order two and higher, the response is here evaluated in terms of characteristic function.Copyright © 2003 by ASME
Sliding mode exponential H<inf>&#x221E;</inf> synchronization of Markovian jumping master-slave systems with time-delays and nonlinea…
2011
This paper investigates the problem of exponential H ∞ synchronization for a class of master-slave systems with both discrete and distributed time-delays, norm-bounded nonlinear uncertainties and Markovian switching parameters. Using an appropriate Lyapunov-Krasovskii functional, some delay-dependent sufficient conditions and a synchronization law which include the master-slave parameters are established for designing a delay-dependent mode-dependent sliding mode exponential H ∞ synchronization control law in terms of linear matrix inequalities. The controller guarantees the H ∞ synchronization of the two coupled master and slave systems regardless of their initial states. A numerical examp…
Non-linear systems under parametric alpha-stable LÉVY WHITE NOISES
2005
In this study stochastic analysis of nonlinear dynamical systems under a-stable, multiplicative white noise has been performed. Analysis has been conducted by means of the Ito rule extended to the case of α-stable noises. In this context the order of increments of Levy process has been evaluated and differential equations ruling the evolutions of statistical moments of either parametrically and external dynamical systems have been obtained. The extended Ito rule has also been used to yield the differential equation ruling the evolution of the characteristic function for parametrically excited dynamical systems. The Fourier transform of the characteristic function, namely the probability den…
Stochastic Response on Non-Linear Systems under Parametric Non-Gaussian Agencies
1992
The probabilistic response characterization of non-linear systems subjected to non-normal delta correlated parametric excitation is obtained. In order to do this an extension of both Ito’s differential rule and the Fokker-Planck equation is presented, enabling one to account for the effect of the non-normal input. The validity of the approach reported here is confirmed by results obtained by means of a Monte Carlo simulation.
A novel approach to nonlinear variable-order fractional viscoelasticity.
2020
This paper addresses nonlinear viscoelastic behaviour of fractional systems with variable time-dependent fractional order. In this case, the main challenge is that the Boltzmann linear superposition principle, i.e. the theoretical basis on which linear viscoelastic fractional operators are formulated, does not apply in standard form because the fractional order is not constant with time. Moving from this consideration, the paper proposes a novel approach where the system response is derived by a consistent application of the Boltzmann principle to an equivalent system, built at every time instant based on the fractional order at that instant and the response at all the previous ones. The ap…
Self-regulation mechanism of an ecosystem in a non-Gaussian fluctuation regime
1996
We study a dynamical model for an ecological network of many interacting species. We consider a Malthus-Verhulst type of self-regulation mechanism. In the framework of the mean field theory we study the nonlinear relaxation in three different cases: (a) towards the equilibrium state, (b) towards the absorbing barrier, (c) at the critical point. We obtain asymptotic behavior in all different cases for the time average of the process. The dynamical behavior of the system, in the limit of infinitely many interacting species, is investigated in the stability and instability conditions and theoretical results are compared with numerical simulations. \textcopyright{} 1996 The American Physical So…