Static Output-feedback Controller Synthesis for Positive Systems under l∞ Performance

This paper investigates the l(infinity)-induced output-feedback controller synthesis problem for discrete-time positive systems. For positive linear systems, a necessary and sufficient condition for stability and l(infinity)-induced performance is first put forward using a group of linear inequalities. Then, on the basis of these inequalities, the conditions on which static output-feedback controllers exist are set up, and to solve these conditions, a method of iterative convex optimization is provided. Moreover, a complete solution to the synthesis problem of the controller is proposed based on linear programming for positive systems with single output or input. Finally, two examples are presented to illustrate and verify the effective and applicable methods derived in this paper.