Reciprocally Convex Approach for the Stability of Networked Control Systems
This chapter deals with the problem of stability analysis for networked control systems via the time-delayed system approach. The network-induced delays are modeled as two additive time-varying delays in the closed-loop system. To check the stability of such particular featured systems, an appropriate Lyapunov–Krasovskii functional is proposed and the Jensen inequality lemma is applied to the integral terms that are derived from the derivative of the Lyapunov–Krasovskii functional. Here, the cascaded structure of the delays in the system enables one to partition the domain of the integral terms into three parts, which produces a linear combination of positive functions weighted by inverses of convex parameters. This is handled efficiently by the authors’ lower bounds lemma that handles the so-called reciprocally convex combination.
KeywordsReciprocally convex combination Delay systems Stability Networked control systems
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0009743).
Poogyeon Park also gratefully acknowledges the LG YONAM Foundation for its financial support through the Professors’ overseas research program for sabbatical research leave at University of Maryland.
- 5.Gu K, Kharitonov VL, Chen J (2003) Stability of time-delay systems, 1st edn. Birkhäuser BostonGoogle Scholar
- 6.Ko JW, Lee WI, Park PG (2011) Delayed system approach to the stability of networked control systems. In: Proceedings of the international multiconference of engineers and computer scientists 2011 (IMECS 2011), Hong Kong. Lecture notes in engineering and computer science, pp 772–774Google Scholar