Robust Control Of The Discrete Time-delay Systems With Uncertain Parameters

Using Lyapunov stability theory, the robust control problem of discrete time-delay systems with uncertain parameters and nonlinear perturbation was investigated in this paper, including the robust stability analysis and the robust controller design for single time-delay and multiple time-delay parameter uncertainty systems, and robust stability analysis of uncertain discrete time-delay systems with nonlinear perturbation. We assume that the uncertain parameters are norm bounded and the nonlinear perturbation satisfies sector condition.1. Robust stability analysisThe criterion condition of robust stability based on Riccati equation is given for the parameter uncertainty systems with single time-delay. The criterion conditions of robust stability based on linear matrix inequality (LMI) are obtained for the parameter uncertainty systems with multiple time-delay and the nonlinear uncertain system with nonlinear perturbation, respectively.2. Robust controller designThe guaranteed cost controller with memory state feedback is designed for the parameter uncertainty systems with single time-delay and state delay, where the controller parameters can be given by the solution of an LMI, and the design method is extended to the case of multiple state delays. For the parameter uncertainty linear discrete systems with both the state delay and the control delay, we employ a linear tramsformation to change the system, and the memoryless state feedback controller is designed for the changed system, thus the robust state feedback controller is obtained for primary system. The controller can be realized by an LMI, and controller parameters are delay-dependent. The memory state feedback H∞controller is given based on an LMI method for the uncertainty linear discrete...