On the H2 and H∞ performance of uncertain positive systems

Abstract

In this paper, robust H2 and H∞ performance analysis of continuous-time and discrete-time positive systems are studied. Necessary and sufficient conditions are presented to ensure H2 and H∞ performance of interval positive systems in terms of semi-definite programming and linear programming, respectively. Based on the direct compatibility of L1 and L∞ induced norms with linear positive Lyapunov functions, the problem is well-established for L1 and L∞ norms, recently. The results of this paper, fill the literature gap by considering robust performance criteria for interval positive systems in terms of H2 and H∞ norms.