BMI-based neurocontroller for state-feedback guaranteed cost control of discrete-time uncertain system

The application of neural networks to the state-feedback guaranteed cost control problem of a discrete-time system that has uncertainty in both state and input matrix is investigated. Based on the bilinear matrix inequality (BMI) design, a class of state feedback controller is newly established, and sufficient conditions for the existence of a guaranteed cost controller are derived. The novel contribution is that the neurocontroller is substituted for the additive gain perturbations. It is newly shown that although the neurocontroller is included in the discrete-time uncertain system, the robust stability for the closed-loop system and the reduction of the cost are attained.