Dual stability conditions for discrete-time positive linear systems with controller failure and polytopic uncertainties

This paper studies the dual stability issues of discrete-time positive linear systems (DPLSs) with controller failure and polytopic uncertainties. First, by utilizing minimum and maximum dwell time approaches, several convex and non-convex stability conditions are obtained for DPLS with controller failure, and the relation of these conditions is revealed. These conditions can be used to check both the global asymptotic stability (GAS) of the original DPLS and the GAS of its dual system. Then, the results are extended to DPLSs with polytopic uncertainties by making use of the convexity of the conditions. All the results are presented in terms of linear programming. Finally, two numerical examples are provided to show the correctness of the results.