Nonlinear Positive Observer Design For Positive Dynamical Systems

In this paper, we address the positive observer design issue for positive dynamical systems. First, for a class of nonlinear positive dynamical systems, we establish a set of sufficient conditions for the design of a general class of positive nonlinear observers. Then, we particularly focus on the new observer design techniques for marginally stable and some unstable continuous positive linear systems. It is shown that there may not always exist a positive observer for such a continuous positive system. Nonetheless, by looking into its equivalent discrete system, the positive observers design can be successfully carried out in the discrete-time domain. This is a natural choice, as many observers and control systems are now implemented digitally on computers. We present new theorems which utilize the structural properties of sampled systems, defined by reducibility. Irreducible structure is explored as the base case and extended to reducible structure. Closed-form designs are presented for full-and reduced-order positive observers, according to the resulting conditions. In particular, for general reducible linear positive systems, a nonlinear reduced-order positive observer is proposed. Numerical examples are provided to illustrate the proposed designs. Copyright © 2010 Watam Press