A sliding mode observer design for uncertain fractional Ito stochastic systems with state delay

ABSTRACT

This paper addresses the robust observer design problem for uncertain time-delay fractional Ito stochastic systems. A sliding surface is proposed and it is shown that state estimates converge towards it and remain there for the subsequent time. Additionally, by constructing a novel Lyapunov functional, a sufficient condition for the stability of the sliding motion of the estimated states is given in the form of Linear Matrix Inequalities (LMIs). It is demonstrated that the state estimates are stabilizable in probability provided that the LMI is feasible. Moreover, a finite-time sliding mode control law based on the estimated states is proposed. Simulation examples are given to show the validity and effectiveness of the results.

KEYWORDS:

• Fractional Ito stochastic systems
• Robust observer
• Linear Matrix Inequalities (LMIs)
• finite-time sliding mode

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

Khosro Khandani http://orcid.org/0000-0002-1762-3541

Additional information

Notes on contributors

Khosro Khandani

Khosro Khandani received his B.Sc. in control engineering from Sahand University of Technology, Tabriz, Iran in 2008. Then he obtained his M.Sc. and Ph.D. degrees in control theory and control engineering from Iran University of Science and Technology, Tehran, Iran and Tarbiat Modares University, Tehran, Iran in 2011 and 2016, respectively. He is currently an assistant professor at Electrical Engineering Department, Faculty of Engineering, Arak University, Arak, Iran. His research interests include fractional order systems and control, stochastic control, multi-agent systems and robust and nonlinear control.