Robust eigenstructure assignment with structured state space uncertainty

Abstract

Recent sufficient conditions for robust stability and robust performance of linear time-invariant systems subject to structured state-space uncertainty are utilized to obtain a robust eigenstructure assignment design method. This new approach optimizes either the sufficient condition for stability or performance robustness while constraining the dominant eigenvalues to lie within chosen regions in the complex plane. This constrained optimization problem is solved by using the sequential unconstrained minimization technique with a quadratic extended interior penalty function. The use of constraints on certain eigenvector entries and the effect of these constraints on robustness and nominal performance are considered. Conservatism of the robustness conditions is reduced by simultaneously introducing a similarity transformation, a positive real diagonal weighting, and a unitary weighting into the design procedure. An example that illustrates the design of a robust eigenstructure assignment controller for a pitch pointing/vertical translation maneuver of the AFTIF-16 aircraft is presented.