Abstract
In Chapter 1, we consider the regularization problem for the linear time-varying discrete-time periodic descriptor systems by derivative and proportional state feedback controls. Sufficient conditions are given under which derivative and proportional state feedback controls can be constructed so that the periodic closed-loop systems are regular and of index at most one. The construction procedures used to establish the theory are based on orthogonal and elementary matrix transformations and can, therefore, be developed to a numerically efficient algorithm. The problem of finite pole assignment of periodic descriptor systems is also studied. In Chapter 2, the inverse eigenvalue problem of constructing real and symmetric square matrices M,C and K of size n × n for the quadratic pencil Q(λ) = λ^2M + λC + K so that Q(λ) has a prescribed subset of eigenvalues and eigenvectors is considered. This chapter consists of two parts addressing two related but different problems.