Parametric control to a type of quasi-linear second-order systems via output feedback

ABSTRACT

This paper considers the design of output feedback control for a type of quasi-linear second-order systems with the time-varying coefficient matrices containing the state variables and a time-varying parameter vector. Based on the solution to a type of second-order generalised Sylvester matrix equations, general complete parameterisation of a quasi-linear output feedback controller is established with respect to the state variables, the time-varying parameter vector, the constant closed-loop system and another two groups of arbitrary parameters, and also for the left and right closed-loop eigenvectors matrices. With the proposed parametric output feedback control, the closed-loop system can be transformed into a constant linear system with desired eigenstructure. Finally, simulation results are provided to illustrate the convenience and effectiveness of application in the general spacecraft rendezvous problem.

KEYWORDS:

• Quasi-linear second-order systems
• parametric control
• eigenstructure assignment
• output feedback
• spacecraft rendezvous

Acknowledgments

The authors thank the Editor-in-Chief and the anonymous reviewers for their helpful comments and suggestions which have helped to improve the quality of this article.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by China Scholarship Council [grant number 2015077900002]; National Natural Science Foundation of China [grant numbers 61333003, 61690212, 61690210].