ON THE SPECTRAL LYAPUNOV APPROACH TO PARAMETRIC OPTIMIZATION OF DISTRIBUTED-PARAMETER SYSTEMS

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.