On pole placement LMI constraints in control design for linear discrete-time systems

Abstract

The paper addresses the problem of constrained pole placement control for discrete-time linear systems. Sufficient conditions for feasibility are outlined in terms of linear matrix inequalities for a D-stable circular region in the complex ś plain. In addition, in the case of state-space control, it is proven that by this way formulated pole placement problem is equivalently uttered using an quadratic integral state constraint, being added to Lyapunov function. Finally, the proposed principle is expanded for systems with polytopic uncertainties.