Stability Conditions for Linear Discrete-Time Positive Switched Systems with Nonuniform Dwell-Time Ranges

This paper deals with linear discrete-time positive switched systems and establishes novel sufficient conditions for global exponential stability under nonuniform dwell-time ranges on switches digraphs. The conditions we introduce in the paper apply to any system, regardless of the stability properties of its discrete modes. We first propose a set of easy to check conditions in the form of linear programming problems which require a test for each admissible dwell-time. Then, we show how such tests can be relaxed for stable and antistable subsystems, on which the conditions need to be checked only on the minimum and maximum dwell-times, respectively.