Robust observer design for two-dimensional discrete positive switched systems with delays

The design problem of the robust positive observer for a class of two-dimensional (2-D) positive discrete switched systems in the presence of delays and uncertainties is considered in this brief. The delays and uncertainties in this brief are assumed to be time-varying and polytopic type, respectively. Firstly, the multiple Lyapunov functional (MLF) approach has been used to formulate some sufficient asymptotical stability conditions for 2-D switched systems with uncertainties, by choosing a suitable co-positive Lyapunov-Krasovskii functional (CPLKF). Secondly, under the assumption that the system states are not measurable, a robust observer design scheme is formulated that helps in the approximation of the corresponding non-negative states. It also ensures the asymptotic convergence of the associated error system. Finally, an appropriate example is discussed to show the usefulness of the proposed results.