Reachability analysis of rational eigenvalue linear systems

Abstract

One of the key problems in the safety analysis of control systems is the exact computation of reachable state spaces for continuous-time systems. Issues related to the controllability and observability of these systems are well-studied in systems theory. However, there are not many results on reachability, even for general linear systems. In this study, we present a large class of linear systems with decidable reachable state spaces. This is approached by reducing the reachability analysis to real root isolation of exponential polynomials. Furthermore, we have implemented this method in a Maple package based on symbolic computation and applied to several examples successfully.

Keywords:

• reachability analysis
• linear systems
• real root isolation
• exponential polynomials
• continued fractions
• interval arithmetic

Acknowledgements

We gratefully thank Prof. Lu Yang, Prof. Wensheng Yu, Dr Min Wu and Dr Zhengfeng Yang for their beneficial and helpful comments on our work. This work is partially supported by the National Natural Science Foundation of China (No. 90718041), Shanghai Leading Academic Discipline Project (No. B412) and the PhD Programme Scholarship Fund of ECNU 2009 (No. 2009056).