Robust stability of closed loop systems resulting from nonsequential MIMO-QFT design

Considered in this paper is the question of whether a compensator realized by the MIMO-QFT (quantitative feedback theory) nonsequential method robustly stabilizes the entire plant family. In order to establish our results, first the classic small gain theorem for robust stability is modified to allow uncertain plant families with poles arbitrarily crossing the imaginary axis, or equivalently, plants in which the number of unstable poles does not remain fixed over all uncertainties. The conventional assumption that the number of unstable poles remain fixed over all uncertainties can be quite restrictive, especially, in the case of plants with structured uncertainties. It is shown that to assure robust stabilty of the closed loop, resulting from the MIMO-QFT nonsequential approach, one more requirement must be added to the procedure. The needed extra condition can be quite naturally incorporated during the execution of the nonsequential technique. As a result the proposed condition does not significantly alter the basic MIMO-QFT nonsequential procedure