A novel approach to L1-induced controller synthesis for positive systems with interval uncertainties

This paper investigates the controller design problem for interval positive systems under L1-induced performance. First, we present the L1-induced performance indicator for positive systems, which fits well into the linear Lyapunov function. Then, the analytic expression is established to obtain the exact value of L1-induced norm and the L1-induced performance characterization is developed. Furthermore, a linear programing based method is proposed to solve the L1-induced controller synthesis problem for positive systems with interval uncertainties. Finally, we provide a numerical example to demonstrate the validity and efficiency of the derived methods.