On construction of sampling patterns for preserving observability/controllability of linear sampled-data systems

ABSTRACT

In this paper, we design a new nonequidistant sampling pattern such that the property of controllability and observability of the linear continuous time systems is preserved during the procedure of the sample and zero-order hold operation. The idea behind the strategy comes from Kronecker's theorem and it is proven that new construction is more effective by requiring less number of sampling times which guarantees controllability and observability of sampled-data system in two dimensional space. Moreover, we provide one application in the concept of controllability of the pendulum in two dimensional space and obtain corresponding digital controls which make the corresponding sampled-data system controllable. Finally, the research is extended to different type of sampling patterns which are compared with the constructed sampling pattern separately.

KEYWORDS:

• Continuous-time invariant systems
• linear sample-data systems
• Kronecker's theorem
• non-equidistant sampling
• observability
• controllability of finite dimensional systems

Acknowledgments

The authors wish to express their sincere thanks to the anonymous reviewers for valuable suggestions which improved the final version of the paper. We also thank to Eric Rogers, Editor-in-Chief of International Journal of Control for his moral support and inspiration for publication of the paper.

Disclosure statement

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