Peak-to-peak robust tracking control for improved disequilibrium cobweb model with multiple time delay effects

This paper proposes a novel design framework of tracking control based on a class of improved disequilibrium cobweb models with exogenous perturbations and multiple time delay states. From the viewpoint of economic control theory, the expected price is designed as a control variable, dynamic feedback control method is used to study the stability of disequilibrium market, the controllability of the market price and the tracking performance of the error between demand and supply. For the considered complex nonlinear cobweb models with perturbations and time delay effects, convex linear matrix inequality (LMI) optimization algorithms and Lyapunov-Krasovskii stability analyzed methods are used to design a generalized feedback controller such that stability of market prices, and tracking performance of the error between demand and supply can be guaranteed. Furthermore, in order to enhance the robustness, the peak-to-peak measure index is applied to optimize the tracking performance. Simulation results show the proposed dynamic approach is effective and adaptable for economic reality.