Output feedback pole-placement in damping region for discrete-time uncertain polytopic systems

Pole placement with specified damping and decay rate is one of the primary criteria for ensuring good transient response. This control design problem has known solutions for continuous-time systems in terms of the linear matrix inequality (LMI) region. However, a systematic solution for a discrete-time system is an open problem due to the non-convexity of the constant damping locus. This paper addresses the problem of placing the closed-loop poles of linear discrete-time uncertain polytopic systems in a constant damping region. The non-convex damping region is approximated to an elliptical segment that represents an LMI region. Criteria for designing state and output feedback (static as well as dynamic) controllers are then derived. The effectiveness of the proposed approach is demonstrated with examples including a boost converter to improve its transient behaviour in the presence of input voltage and load variations.