Null controllable region of delta operator systems subject to actuator saturation

ABSTRACT

In this paper, we give exact description of null controllable regions for delta operator systems subject to actuator saturation. The null controllable region is in terms of a set of extremal trajectories of anti-stable subsystems. For the delta operator system with real eigenvalues or complex eigenvalues, the description is simplified to an explicit formula which is used to characterise the boundary of a null controllable region. The relations of null controllable regions are shown separately for continuous-time systems, discrete-time systems and delta operator systems. Two numerical examples are given to illustrate the effectiveness of the proposed techniques on null controllable regions.

Keywords:

• Null controllable region
• delta operator system
• actuator saturation
• time-reversed system

Acknowledgments

The authors would like to thank the anonymous reviewers for their detailed comments which helped to improve the quality of the paper. The work was supported by the National Basic Research Program of China (973 Program) (2012CB720000). The work was also supported by the National Natural Science Foundation of China (61203023, 61225015, 61473024, 61573301), the Hebei Provincial Natural Science Fund (E2014203122, F2013203092), and the Ph.D. Programs Foundation of Ministry of Education of China (20111101110012).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was supported by the National Basic Research Program of China (973 Program) [grant number 2012CB720000]. The work was also supported by the National Natural Science Foundation of China [grant number 61203023], [grant number 61225015], [grant number 61473024], [grant number 61573301]; the Hebei Provincial Natural Science Fund [grant number E2014203122], [grant number F2013203092]; and the Ph.D. Programs Foundation of Ministry of Education of China [grant number 20111101110012].