On the Spectral-Lyapunov Approach to Parametric Optimization of Distributed-Parameter Systems

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Abstract
The paper is devoted to the discussion of the Riesz-bases application in the analysis of distributed-parameter systems controlled by a finite-dimensional or conventional controller. Both boundary control and boundary observation are allowed. The Riesz bases are constructed from a system of eigenfunctions of the closed-loop system operator. On the basis of the results obtained, they are expected to be an effective tool in proving that the closed-loop system is well-posed; i.e. they give rise to a C 0 -semigroup. These bases also enable us to construct Lyapunov functionals in the form of series expansions. The analysis is illustrated by a completely worked-out example where the proportional controller setting is optimized with respect to the ISE criterion. The controller is applied to a parabolic plant modelling a resistive—capacitative (noninductive) direct-current transmission line.

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