Academy & Industry Research Collaboration Center (AIRCC)

Volume 9, Number 7, June 2019

An Approach to Tracking Problem for Linear Control System Via Invariant Ellipsoids Method


Mikhail Khlebnikov, V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Russia


In this paper, a simple yet universal approach to the tracking problem for linear control systems via the linear static combined feedback is proposed. The approach is based on the invariant ellipsoid concept and LMI technique, where the optimal control design reduced to finding the minimal invariant ellipsoid for the closed-loop system. With such an ideology, the control design problem directly reduces to a semidefinite programming and one-dimensional minimization. Another attractive property of the proposed approach is that it is equally applicable to discrete-time control systems. The efficacy of the technique is illustrated via a benchmark problem.


Linear Control Systems, Tracking Problem, Invariant Ellipsoids, LMIs