On the stabilisation of unknown steady states of chaotic systems

In this paper we study the problem of stabilisation of unknown steady states of chaotic systems using linear controllers, which has recently received some attention in the physics literature. A complete characterisation of stabilising linear state feedback controllers of minimal dimension is given. For the case of output feedback stabilisation, some partial results are derived. A detailed investigation of the controller implementation using an OGY-type methodology on a controlled Lorenz system is given.