Functional observer-based sliding mode controller design for discrete-time stochastic LTI systems with unmatched uncertainty

ABSTRACT

Discrete-time sliding mode control is one of the most prominent robust control technique to stabilise systems. However, the assumption of full state feedback being available is seldom satisfied in practice. This paper presents the functional observer-based sliding mode controller (SMC) design for discrete-time stochastic systems with unmatched uncertainty. A disturbance-dependent sliding function method is proposed such that the effect of unmatched uncertainty of the system is minimised. Furthermore, SMC is calculated using the functional observer method. Finally, a simulation example is given to show the effectiveness of the proposed method.

Keywords:

• Discrete-time stochastic systems
• unmatched uncertainty
• sliding mode controller
• linear functional observer

Acknowledgements

The authors would like to thank the editors and the anonymous reviewers for a number of helpful comments, which improved the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Satnesh Singh  http://orcid.org/0000-0002-2827-1166

S. Janardhanan  http://orcid.org/0000-0003-3678-6300

Additional information

Notes on contributors

Satnesh Singh

Satnesh Singh received his B. Tech degree in Electrical & Electronics Engineering from Uttar Pradesh Technical University Lucknow, India (2009), and M. Tech degree in signal processing & control, Electrical Engineering Department from National Institute of Technology Hamirpur, India (2011). Currently, he is pursuing PhD degree in Control & automation from Department of Electrical Engineering, Indian Institute of Technology Delhi, India. His research interests include linear and non-linear systems in sliding mode control, stochastic system, time-delay and functional observers. E-mail: [email protected]

S. Janardhanan

Dr. S. Janardhanan received his M.Tech and Ph.D in Systems and Control Engineering from Indian Institute of Technology Bombay in 2002 and 2006, respectively. Currently, he is a faculty with the Department of Electrical Engineering, Indian Institute of Technology Delhi. He has over 100 publications in journals and conferences of international repute to his credit. His research interests include discrete-time systems, model order reduction, sliding mode control and robotics. E-mail: [email protected]