Stabilization for a Class of Positive Bilinear Systems

In this letter, we consider stabilizing control design for a class of positive bilinear systems. Positivity allows us to employ a max-separable function for Lyapunov analysis, enabling to estimate a region of attraction as a box, which is particularly useful for heat exchangers. We take the summation of max-separable functions with respect to the state and input as a Lyapunov candidate and design a dynamic stabilizing controller. Moreover, employing a quadratic function with respect to the input and integral action of a performance output, we propose another dynamic stabilizing controller which can additionally regulate the output.