Guaranteed cost PI control for uncertain discrete-time systems with additive gain

This paper investigates a novel design method for robust proportional-integral (PI) control that is based on the guaranteed cost control (GCC) problem for a class of uncertain discrete-time systems with additive gain. On the basis of linear matrix inequality (LMI), a class of fixed PI controller parameters is obtained, and some sufficient conditions for the existence of the GCC are derived. A novel concept is that the fixed PI controller parameters are combined with additive gain such as that in neural networks (NNs) to enhance the transient stability. Although the additive gain is included in the feedback systems, both the stability of closed-loop systems and desired transient response are obtained. Finally, the experimental result demonstrates that the transient response can be appropriately changed by adjusting the additive gain.