L1-induced Performance Analysis and Sparse Controller Synthesis for Interval Positive Systems

Abstract

This paper is concerned with the design of L1- induced sparse controller for continuous-time positive systems with interval uncertainties. A necessary and sufficient condition for stability and L1-induced performance of positive linear systems is proposed in terms of linear inequalities. Based on this, conditions for the existence of robust state-feedback controllers are established. Moreover, the total number of all the nonzero elements of the controller gain is to be minimized, while satisfying a guaranteed level of L1-induced performance. Then, we propose an ℓ1-minimization problem to relax the ℓ0 objective function for optimization and an iterative convex optimization approach is developed to solve the conditions. Finally, an illustrative example is provided to show the effectiveness and applicability of the theoretical results.