Sequential eigenstructure assignment with maximal stability robustness

Abstract

The maximal stability robustness problem for a linear, time‐invariant, multi‐input system's state equations involves the design of a state‐feedback gain controller which simultaneously achieves eigenvalue assignment and maximal stability robustness. In this paper, we propose a practical sequential eigenstructure assignment scheme for designing a parametric state‐feedback gain matrix, which sequentially shifts a prescribed set of self‐conjugate multiple eigenvalues to the closed‐loop system in groups. The spectrum‐invariant free parameters are parameterized explicitly in terms of the extra degrees of freedom offered by the state‐feedback controller matrix beyond eigenvalue shifting, and can be exploited to maximize the largest spectral norm of an additive uncertainty in the closed‐loop system matrix, so that stability is guaranteed. A numerical example of the design method is illustrated.