PID Output-Feedback Control and Filtering for Positive Roesser System

This paper considers the output-feedback-based proportional-integral-derivative (PID) control and filtering problems for the discrete-discrete Roesser system with disturbances. A PID output-feedback controller, where the integral loop is with fixed time-window, is first constructed for the two-dimensional system. By means of co positive Lyapunov function approach, sufficient conditions are proposed to ensure that the resulting closed-loop system is positive, exponentially stable and has an l(1)-gain bound ?. In addition, the gains of desired PID controller are then appropriately parameterized by solutions to certain linear programming problems. An illustrated example is provided to show effectiveness of the PID controller designed.