H∞ estimation for non-linear positive switched systems with time-varying delay

Abstract

Abstract For non-linear positive switched systems (NPSSs) with time-varying delay, the $H_{\infty }$ estimation problem is addressed in this paper. Firstly, in light of T-S fuzzy modeling method, the considered NPSS is equivalently transformed into a switched positive T-S fuzzy system. Then, a less conservative $H_{\infty }$ performance co1ndition is provided for the error system via presenting a new piecewise quadratic copositive Lyapunov–Krasovskii functional. Furthermore, an observer is constructed to make the underlying system exponentially stable with a preset $H_{\infty }$ performance and an iterative optimization algorithm is proposed to obtain the observer parameters. To verify the effectiveness of the theoretical results, two examples are finally presented.