Finite-Time Non-Fragile Control of a Class of Uncertain Linear Positive Systems

The finite-time non-fragile control scheme has received great interest because of its robustness to the controller gain errors. In this paper, we intend to study the finite-time non-fragile control problems for a class of linear positive systems with uncertainties. It devises an appropriate non-fragile control law, such that the closed-loop system is positive and stabilizable and satisfies the given $H_{\infty }$ performance in a specified time interval. The main issue is to give a sufficient condition for the solution of the designed finite-time non-fragile $H_{\infty }$ controller associated with the several control techniques applied to the positive system. The design result is described as an optimization problem that can be expressed through a couple of linear matrix inequalities. In the end, we use a practical RL circuit model to evaluate the performance of the proposed controller.