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.