On analytic interpolation with non-classical constraints for solving problems in robust control

TL;DR

This paper introduces a novel approach for robust control stabilization by solving a non-classical analytic interpolation problem with frequency-dependent constraints, providing a new method for controller synthesis in uncertain systems.

Contribution

It develops a new non-classical interpolation framework with frequency-dependent constraints and offers an approximate solution algorithm for robust control design.

Findings

Successful numerical example with uncertain gain, phase, and delay

Derived sufficient conditions for the interpolation problem's solvability

Proposed an approximate algorithm applicable to controller synthesis

Abstract

In this work we consider robust stabilization of uncertain dynamical systems and show that this can be achieved by solving a non-classically constrained analytic interpolation problem. In particular, this non-classical constraint confines the range of the interpolant, when evaluated on the imaginary axis, to a frequency-dependent set. By considering a sufficient condition for when this interpolation problem has a solution, we derive an approximate solution algorithm that can also be used for controller synthesis. Finally, the theory is illustrated on a numerical example with a plant with uncertain gain, phase, and output delay.