Finite-time annular domain robust guaranteed cost control of interval positive linear systems

Abstract

The issue of finite-time annular domain robust guaranteed cost control of positive linear systems with interval uncertainties is investigated in this paper. First, by using the linear copositive Lyapunov function, a sufficient condition for the existence of state feedback controller is given to ensure the positivity and finite-time annular domain robust stability of the closed-loop system, and guarantee the cost function is no more than a given upper bound. The corresponding controller design method is derived based on linear programming technique. Then, an optimisation algorithm is further developed to obtain the optimal guaranteed cost controller, which is convenient to be computed. Finally, a numerical example and an application example are given to demonstrate the effectiveness of theoretical results.

Keywords:

• Linear copositive Lyapunov function
• finite-time annular domain robust stability (FTADRS)
• guaranteed cost control
• interval uncertainties
• positive linear systems (PLSs)

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant numbers 62373204, 61977043 and 62003181], the Young Taishan Scholars Program of Shandong Province of China [grant number tsqn202211202], the Research Foundation for Advanced Talents of Qilu University of Technology [grant numbers 2023RCKY148 and 2023RCKY149], and the Cultivating Foundation of Qilu University of Technology [grant number 2022PYI010], and the Youth Innovation Science and Technology Support Plan of Colleges in Shandong Province [grant number 2022KJ131].