Discrete-time regional pole-placement using convex approximations: Theory and application to a boost converter

The problem of allocating the closed-loop poles of linear systems in specific regions of the complex plane defined by discrete time-domain requirements is addressed. The resulting non-convex set is inner-approximated by a convex region described with linear matrix inequalities. The proposed approach enables a trade-off between computational complexity in terms of mathematical program size and conservativeness. A case study is then carried out on a step-up power converter, comparing three different techniques. Experimental results are provided to show how the proposed control strategy can be employed to enhance its start-up and transient responses when subjected to input voltage and load variations.