Observer-based controller for positive polynomial systems with time delay

This paper deals with some synthesis problems for a class of positive polynomial systems with time delay, for which the state vector takes nonnegative values whenever the initial conditions are nonnegative. First, the synthesis of state feedback controllers is solved using a Lyapunov-Krasovskii approach, including the requirement of positiveness. In a second part, observers are included. In both cases, the design conditions are presented in terms of sum of squares, which can be numerically and symbolically solved via SOSTOOLS and a semidefinite program solver. Finally, four numerical examples are given to illustrate the proposed approach.