A transformed descriptor approach to stabilizability of constrained parallel splitting systems

This paper presents the application of the asymptotically positive realness constraint (APRC) in the stabilization for interconnected systems with a descriptor system approach. Handling parallel redundant subsystems that have unknown splitting ratios is an essential part of this development. We have introduced the parallel masking technique in previous work whereby the APRC and the dissipation inequalities are applied to different hierarchies of subsystem interconnections. In this work, the dissipativity criterion for parallel splitting systems is derived from a transformed descriptor system with the employment of a specially structured storage function. The pre-heating an desilication unit operation in an alumina refinery is simulated to illustrate the theoretical results.