NONLINEAR REGULATION OF A LORENZ SYSTEM BY FEEDBACK LINEARIZATION TECHNIQUES

In this paper we analyze some dynamical properties of a chaotic Lorenz system driven by a control input. These properties are the input-state and the input-output feedback linerazability, the stability of the zero dynamics, and the phase minimality of the system. We show that the controlled Lorenz system is feedback equivalent to a controllable linear system. We also show that the zero dynamics are asymptotically stable when the output is an arbitrary state. These facts allow designing control laws such that the closed-loop system has asymptotically stable equilibrium points with dynamic behavior free from chaotic transients. The controllers are robust in the sense that the closed-loop system is stable and non chaotic around a nominal set of parameter values. The results also show that the proposed controllers give better responses compared to linear algorithms obtained from standard linearization techniques, and exhibit a good performance even when the control input is bounded.