Robust overlapping output feedback control design in uncertain systems with unknown uncertainty bounds

This paper deals with stabilisability of overlapping uncertain linear systems with fixed modes by overlapping static output feedback controllers. The uncertainties are assumed to be time-varying and norm-bounded. The fixed modes arise from natural changes in the physical system parameters due to operational conditions. The approach used in this paper is based on the inclusion principle where the system is first expanded into a weakly interconnected system that preserves all of the properties of the original system. Then, an Iterative Linear Matrix Inequality (ILMI) algorithm is proposed to find (i) the maximum upper bounds on the 2-norm of the uncertainties such that the uncertain expanded system is robustly stabilisable with a decentralised static output feedback control, and (ii) a robust decentralised guaranteed static output feedback cost controller for the expanded system. Finally, both the robust decentralised controller and the upper bounds are contracted to a robust overlapping guaranteed cost controller and upper bounds on the uncertainties of the original system, respectively. A numerical example is provided to illustrate the design approach.