Transient response shaping in H∞ control by eigenstructure assignment to convex regions

In this paper, eigenstructure assignment to a set of convex regions is proposed. Transient response shaping of H. control via the proposed approach is also discussed. Firstly, closed-loop eigenvalue (pole) assignment to a set of convex Lyapunov regions is proved via rank-one LMI (Linear Matrix Inequality) approach. Secondly, as the first result of this paper, eigenstructure assignment to convex regions is proved. Closed-loop eigenvector misalignment angle bound condition is reduced to a rank-one LMI condition and easily combined with the eigenvalue assignment problem. Finally, as the second result of this paper, transient response shaping in H. control by the presented approach, is proposed. By using the presented loose assignment approach, design trade-off between the closed-loop eigenstructure assignment and H. condition can be easily considered. These two conditions are connected via enhanced LMI characterization.