Robust Eigenvalue Assignment via Sampled State-Feedback for Linear Polytopic Discrete-Time Periodic Systems

This work deals with the robust eigenvalue assignment problem for periodic discrete-time systems with polytopic uncertainties. By employing a sampled state-feedback control law, a suitable time-invariant reformulation describing a period ahead dynamics associated with the uncertain periodic system is obtained. The obtained results are based on a special class of parameter-dependent Lyapunov functions that adequately cope with the one period ahead dynamics. The robust eigenvalue assignment problem is solved via a convex problem. The proposed conditions ensure that all eigenvalues of the proposed time-invariant reformulation subject to uncertainties are within a specified circular region in the complex plane. Numerical simulations are presented to illustrate the effectiveness of the proposed conditions.