Distributed static output feedback control for interconnected systems in finite‐frequency domain

Abstract

This paper aims at designing a distributed static output feedback (DSOF) controller for the interconnected system in finite‐frequency domain. Motivated by the fact that the signal transmitting process is usually affected by surrounding environments, the interconnection communication between subsystems are assumed to be non‐ideal. By introducing some dilated multipliers into the extended condition that guarantees the well‐posedness, stability and finite‐frequency ${\mathcal{H}}_{\infty }$ performance of non‐ideally interconnected systems, a new equivalent condition is derived, which is more effective for parameterizing the DSOF controller. A two‐stage approach is then developed for constructing a DSOF controller: design an initial distributed full information (DFI) controller first and then derive a desired DSOF from the DFI controller. Moreover, two iterative linear matrix inequality based algorithms are proposed to improve the solvability of the DFI controller and DSOF controller design problems. Finally, an example is given to show the effectiveness of the proposed two‐stage DSOF controller design method.