Robust H2 control of ladder circuits modeled as a subclass of 2D systems

Abstract

Spatially interconnected systems are the special case of 2D systems, since there exist 2 independent variables in the model. In the paper RLC ladder circuit uncertain model is taken as a particular case of such systems. Due to the model structure and uncertainties solving problems of stability testing and stabilization for such models requires developing its own, 2D based, approach. Hence on, a short introduction into 2D system theory is provided, then a methodology towards stability analysis and stabilizing controller design with the application of Linear Matrix Inequalities (LMI) techniques are presented. The main results of this paper is providing the solution for problems of the robust control and $H_{2}$ robust control of ladder circuits in terms of LMIs.