Robust Stability and Stabilization of n-D Systems

Abstract In this paper, first, the stability margin and stabilizability margin of multidimensional (nD) systems are considered. In particular, the concept of stabilizability margin is introduced for the first time and it is defined to be the largest stability margin that a closed-loop feedback system can reach by menas of any stabilizing compensator. The investigation of stabilizability margin is of special interest in nD system theory, as such a problem does not happen to a conventional 1D system without hidden mode. A general computational algebraic procedure is then proposed, based on quantifier elimination formulation and cylindrical algebraic decomposition method, for both computation of the stability/stabilizability margins and construction of a stabilizing compensator which can reach a stability margin for the resulant closed-loop system as close to the stabilizability margin as desirable.