We show that weak L-p dissipativity implies strong L-infinity dissipativity and therefore implies the existence of global attractors for a general class of reaction-diffusion systems. This generalizes the results of A...
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We show that weak L-p dissipativity implies strong L-infinity dissipativity and therefore implies the existence of global attractors for a general class of reaction-diffusion systems. This generalizes the results of Alikakos and Rothe. The results on positive steady states (especially for systems of three equations) in our earlier work (J. Differential Equations 130 (1996). 59-91) are improved. (C) 1998 Academic Press.
We present a method for obtaining evolution operators for linear quantum trajectories. We apply this to a number of physical examples of varying mathematical complexity, in which the quantum trajectories describe the ...
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We present a method for obtaining evolution operators for linear quantum trajectories. We apply this to a number of physical examples of varying mathematical complexity, in which the quantum trajectories describe the continuous projection measurement of physical observables. Using this method we calculate the average conditional uncertainty for the measured observables, being a central quantity of interest in these measurement processes.
This paper is concerned with a design of finite-dimensional H ∞ controllers for semilinear distributed parameter systems whose linear principal parts are of modal type. First, a finite-dimensional H ∞ controller is ...
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This paper is concerned with a design of finite-dimensional H ∞ controllers for semilinear distributed parameter systems whose linear principal parts are of modal type. First, a finite-dimensional H ∞ controller is constructed for the linear distributed parameter system by using a previous result of the author. Then, it is shown that the finite-dimensional H ∞ controller works as a finite-dimensional H ∞ controller for the given semilinear distributed parameter system under certain conditions with respect to the nonlinear perturbation.
This paper introduces a stability radius for a wide class of linear infinite-dimensional time-varying systems under structured time-varying perturbations. A framework is presented that allows the same degree of unboun...
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This paper introduces a stability radius for a wide class of linear infinite-dimensional time-varying systems under structured time-varying perturbations. A framework is presented that allows the same degree of unboundedness in the perturbations as in the generator of the nominal model.
The fundamental matrix of the 5-by-5 system of partial differential operators describing linear thermodiffusion inside elastic media is - by a standard procedure - expressible through the fundamental solution of its d...
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This paper is concerned with a design of finite-dimensional H ∞ time-varying controllers for infinite-dimensional linear time-varying systems whose homogeneous parts are of modal type. A finite-dimensional model is d...
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This paper is concerned with a design of finite-dimensional H ∞ time-varying controllers for infinite-dimensional linear time-varying systems whose homogeneous parts are of modal type. A finite-dimensional model is derived for the infinite-dimensional system, and an H ∞ controller is constructed for the finite-dimensional model. Then, it is shown that a controller, which consists of a residual mode filter and the H ∞ controller mentioned above becomes a finite-dimensional H ∞ controller for the given infinite-dimensional system if the order of residual mode filter is chosen sufficiently large.
The fundamental matrix of the system of partial differential operators that governs the diffusion of heat and the strains in elastic media is represented by simple definite integrals and power series. For the elements...
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The fundamental matrix of the system of partial differential operators that governs the diffusion of heat and the strains in elastic media is represented by simple definite integrals and power series. For the elements of this matric, the constant and the linear term in the Taylor series about 0 with respect to the coupling constant are expressed explicitly by error functions, elementary functions, and delta functions.
Liapunov equations for time-varying linear systems in Hilbert space are given. This generalizes Datko's result for semigroups. Time-varying linear stochastic systems are also considered and analogous results are o...
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Liapunov equations for time-varying linear systems in Hilbert space are given. This generalizes Datko's result for semigroups. Time-varying linear stochastic systems are also considered and analogous results are obtained.
Using a recent result of Castaing and Clauzure on the lower semicontinuity of integral functionals, we prove the existence of an optimal control for a broad class of nonlinear infinite-dimensional control systems. An ...
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Using a recent result of Castaing and Clauzure on the lower semicontinuity of integral functionals, we prove the existence of an optimal control for a broad class of nonlinear infinite-dimensional control systems. An example of a distributed parameter system is worked in detail.
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