A polynomial approach to decentralised control analysis and design

The analysis and synthesis problem of decentralised control is considered in this paper. First, it is shown that the fixed modes of the plant are the roots of the greatest common unstable divisor of a set of specific polynomials, and all these polynomials and the closed-loop characteristic polynomial are explicitly given. Second, if the system is decentralisedly stabilisable, then a novel method is presented to design the local dynamic feedback controllers such that the overall decentralised control system is stable. Third, the so-called decentralised concurrent stabilisation problem (DCSP) is investigated and a new algorithm for solving the DCSP problem is developed. Several examples are included to illustrate the results.