Linear Controllers for the Stabilization of Unknown Steady States of Chaotic Systems

The problem of stabilization of unknown steady states of chaotic systems by means of linear controllers is studied. A complete solution of the problem is given for the case of state feedback stabilization. For the case of output feedback stabilization, some partial results are given. The paper shows that the control theoretic concepts of controllability, stabilizability and root-locus are instrumental in the solution of the problem. All results are illustrated by means of the stabilization of unknown steady states of a controlled Lorenz system