Chaotifying a stable LTI system by tiny feedback control

Abstract

The problem of making a stable linear time-invariant (LTI) system chaotic by using state-feedback control of arbitrarily small magnitude is studied. The feedback controller used is a simple sawtooth or modulo function of the system states, which can lead to uniformly bounded state vectors of the controlled system with positive Lyapunov exponents, thereby yielding chaotic dynamics. In fact, we mathematically prove that this controlled system is chaotic in the sense of Li and Yorke (1975).