A decentralized stability criterion for two-level systems with optimization in the feedback loop
Peter P. Groumpos, Andreas V. Pagalos, G.S. Stavropoulos · 2005
In this paper the stabilization of a linear decentralized Large Scale System (LSS) of the BAS form is considered. The block arrow structure (BAS) of the A matrix appears in an LSS which consists of N linear subsystems Sl' S2' S N in a lower hierarchical level, interconnected through a common linear subsystem So' in a higher hierarchical level when the N subsystems are not connected to each other. The continuous state -space model and controlling algorithm of such a system is presented. In the first part of the paper a stability criterion for the overall system is developed. In this way we can conclude that the closed loop system is stable by solving a set of Lyapunov equations, one for each subsystem, and then examining whether a predetermined set of conditions is satisfied. The next part of the paper describes the optimization of the feedback gain using a gradient typc algorithm for the adaptation of the gain in the constrained space of the BAS feedback gains. Thus, a near optimal solution is obtained, which keeps all the BAS appealling characterisics and is closer to the optimal solution than any other previous aproach. Numerical examples are given in order to demonstrate the theoretical results of this work.