In this paper, we study the problem of the asymptotic property of the norm of input-output operators related to a class of singularly perturbed stochastic linear systems. The system is under perturbation of multiplica...
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In this paper, we study the problem of the asymptotic property of the norm of input-output operators related to a class of singularly perturbed stochastic linear systems. The system is under perturbation of multiplicative white noise. By using reduction order and boundary layer techniques, it is shown that the norm of the operator of the perturbed system is less than a given number gamma when the small perturbation tends to zero if both the related norms of the reduced subsystem and the boundary layer subsystem are less than gamma. Furthermore, a stabilizing robust controller is designed, which is independent of perturbation epsilon.
In this paper, we study the robust stability of implicit dynamic equations with causal operators on time scales. First, we investigate the solvability of these dynamic equations and then consider the preservation of s...
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In this paper, we study the robust stability of implicit dynamic equations with causal operators on time scales. First, we investigate the solvability of these dynamic equations and then consider the preservation of stability under small perturbations. An L-p version of Bohl-Perron principle for implicit dynamic equations is also studied.
We consider a recursive iterative algorithm for identification of parameters of the Preisach model, one of the most commonly used models of hysteretic input-output relationships. This online algorithm uses a simple ru...
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We consider a recursive iterative algorithm for identification of parameters of the Preisach model, one of the most commonly used models of hysteretic input-output relationships. This online algorithm uses a simple rule for updating the values of the piecewise constant density function in the switching region at each time step. The so-called persistent excitation condition has been shown to play an important role for convergence of recursive iteration schemes when input-output data are generated by a deterministic input (such as, for example, a periodically repeated sequence of test inputs prescribed by the classical Mayergoyz identification algorithm). In this work, we assume that the input randomly fluctuates and these fluctuations can be described by a stochastic Markov process. Assuming that accurate measurements of the input and output are available, we prove the exponential convergence of the recursive identification algorithm, estimate explicitly the convergence rate, and explore which properties of the stochastic input and the algorithm affect the guaranteed convergence rate. An analogue of the persistent excitation condition suitable for analysis of stochastic Markov inputs is established. Numerical examples that test the convergence of the algorithm in the case of a time-dependent density function and in the presence of measurement noise are presented.
In this paper, the problem of robust stability for linear time-varying implicit dynamic equations is generally studied. We consider the effect of uncertain structured perturbations on all coefficient matrices of equat...
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In this paper, the problem of robust stability for linear time-varying implicit dynamic equations is generally studied. We consider the effect of uncertain structured perturbations on all coefficient matrices of equations. A formula of stability radius with respect to dynamic structured perturbations acting on the right-hand side coefficients is obtained. In case where structured perturbations affect on both derivative and the right-hand side, the lower bounds for the stability radius are derived. The results are novel and extend many previous results about robust stability for time-varying ordinary differential/difference equations, time-varying differential algebraic equations and time-varying implicit difference equations.
This paper is concerned with the robust stability for linear time-varying differential-algebraic equations. We consider the systems under the effect of uncertain dynamic perturbations. A formula of the structured stab...
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This paper is concerned with the robust stability for linear time-varying differential-algebraic equations. We consider the systems under the effect of uncertain dynamic perturbations. A formula of the structured stability radius is obtained. The result is an extension of a previous result for time-varying ordinary differential equations proven by Birgit Jacob [B. Jacob, A formula for the stability radius of time-varying systems, J. Differential Equations 142 (1998) 167-187]. (c) 2006 Elsevier Inc. All rights reserved.
Representation and boundedness properties of linear, right-shift invariant operators on half-line Bessel potential spaces (also known as fractional-order Sobolev spaces) as operator-valued multiplication operators in ...
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Representation and boundedness properties of linear, right-shift invariant operators on half-line Bessel potential spaces (also known as fractional-order Sobolev spaces) as operator-valued multiplication operators in terms of the Laplace transform are considered. These objects are closely related to the input-output operators of linear, time-invariant control systems. Characterisations of when such operators map continuously between certain interpolation spaces and/or Bessel potential spaces are provided, including characterisations in terms of boundedness and integrability properties of the symbol, also known as the transfer function in this setting. The paper considers the Hilbert space case, and the theory is illustrated by a range of examples.
Hyperbolicity of linear systems of difference and differential equations is a robust property. We provide a quantity to measure the maximal size of perturbations under which hyperbolicity is preserved. This so-called ...
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ISBN:
(纸本)9781461473336;9781461473329
Hyperbolicity of linear systems of difference and differential equations is a robust property. We provide a quantity to measure the maximal size of perturbations under which hyperbolicity is preserved. This so-called hyperbolicity radius is calculated by two methods, using the transfer operator and the input-output operator.
This paper is concerned with a formula of stability radii for a linear implicit difference equation (LIDEs for short) varying in time with index-1 under structured parameter perturbations. It is shown that the l(p)-re...
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This paper is concerned with a formula of stability radii for a linear implicit difference equation (LIDEs for short) varying in time with index-1 under structured parameter perturbations. It is shown that the l(p)-real and complex stability radii of these systems coincide and they are given by a formula of input-output operators. The result is an extension of a previous result for time-varying ordinary differential equations [7].
This paper studies synchronization mechanisms for networks of biological *** network is made up of compartments(e.g.,*** in a cell culture) which consist of heterogeneous subsystems(e.g.,reaction pathways) interconnec...
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ISBN:
(纸本)9781509009107
This paper studies synchronization mechanisms for networks of biological *** network is made up of compartments(e.g.,*** in a cell culture) which consist of heterogeneous subsystems(e.g.,reaction pathways) interconnected by internal *** compartments are,in turn,interrelated through common *** on this structural foundation,synchronization conditions are provided from operator-theoretic view of point,which involve the input-output properties of individual compartment together with topological structure of underlying ***,as an additional goal,the paper also provides synchronization criterion for the networks modeled in the formalism of ***,the proposed theory finds bio-chemical applications in the networks of toggle switches and repressilators,respectively.
Characterizations of the stability radii of a stable linear stochastic Itô system with respect to structured stochastic multiperturbations are given. We extend some results in [1], [2]
Characterizations of the stability radii of a stable linear stochastic Itô system with respect to structured stochastic multiperturbations are given. We extend some results in [1], [2]
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