Robust and minimum norm pole assignment with periodic state feedback

A computational approach is proposed to solve the minimum norm or robust pole assignment problem for linear periodic discrete-time systems. The proposed approach uses a periodic Sylvester-equation-based parametrization of the periodic pole assignment problem and exploits the nonuniqueness of the problem by imposing conditions on the norm of the resulting periodic state feedback or on the condition numbers of the periodic eigenvector matrices of the closed-loop system. The solution method relies on using gradient search methods on suitably defined cost functions. Explicit expressions of the gradients of cost functions are derived, and the efficient evaluation of the cost functions and gradients is discussed. Numerical examples illustrate the effectiveness of the proposed approach.