Equivalent conditions of finite-time time-varying output-feedback control for discrete-time positive time-varying linear systems

This paper studies the issue of finite-time time-varying output-feedback control for positive time-varying discrete-time linear systems. Finite-time stability for the systems with positivity is defined. To make sure that the system can be finite-time stable with positivity, an analysis condition is established first, and then two conditions for solving the static output-feedback controller are derived in this work where all the obtained results are necessary and sufficient conditions. An iterative algorithm for solving the controller is developed and finally, an example is given in the simulation to verify the effectiveness of our results and algorithm.