A structural approach to robust control

We consider the problem of stabilizing linear stationary parametrically uncertain systems with a guaranteed stability margin. The methodology of our approach is based on the synthesis of superstable closed systems, done with the procedures derived from the block control principle and their modifications, the procedures consisting of sequential establishment of local connections in elementary blocks that provide for the superstability of each block and the closed system as a whole in the new coordinate basis. The fact that the notion of superstability is formulated in terms of the elements of the system matrix based on inequalities lets us provide for robust stability for all admissible values of indefinite parameters in such systems. The robust control algorithms that we have developed are applicable to a practically significant class of linear systems which, given that parameters change in known ranges, preserve structural controllability properties defined by the nominal system.

Presented by the member of Editorial Board: A. P. Kurdyukov