Reliable control for linear systems with time-varying delays and parameter uncertainties

ABSTRACT

In this paper, reliable control for linear systems with time-varying delays and parameter uncertainties is considered. By constructing newly augmented Lyapunov–Krasovskii functionals and utilizing some mathematical techniques such as Leibnitz's rule, Schur's complement, reciprocally convex combination, and so on, a reliable controller design method for linear systems with time-varying delays and parameter uncertainties will be suggested in Theorem 1. Based on the result of Theorem 1, a non-reliable stabilization criterion will be presented in Corollary 1. Theorem 1 and Corollary 1 are derived within the framework of linear matrix inequalities(LMIs) which can be easily solved by utilizing various optimization algorithms. Two numerical examples are included to show the effectiveness and necessity of the proposed results.

KEYWORDS:

• Reliable control
• time-varying delays
• parameter uncertainties
• Lyapunov method

2010 AMS SUBJECT CLASSIFICATION:

• 93C05

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0009273). This work was also supported by the Human Resources Development of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Trade, Industry & Energy (no. 20144030200450).