Open AccessDiscrete‐time sliding mode control with state bounding for linear systems with time‐varying delay and unmatched disturbances
Author(s) -
That Nguyen Dinh,
Ha Quang P.
Publication year - 2015
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2014.1151
Subject(s) - control theory (sociology) , bounding overwatch , discrete time and continuous time , sliding mode control , computer science , state (computer science) , mode (computer interface) , state observer , control (management) , control engineering , engineering , mathematics , nonlinear system , algorithm , physics , artificial intelligence , statistics , quantum mechanics , operating system
This study is concerned with the problem of quasi‐sliding mode control design for a class of discrete‐time systems with time‐varying delay and unmatched disturbances. On the basis of the Lyapunov–Krasovskii method, combined with the reciprocally convex approach, sufficient conditions for the existence of a stable sliding surface are first derived in terms of matrix inequalities. These conditions also guarantee that the state trajectories of the reduced‐order system are exponentially convergent within a ball whose radius can be minimised to deal with the effects of time‐varying delay and disturbances. A robust quasi‐sliding mode control scheme is then developed to drive the system state trajectories towards that ball in a finite time and maintain them therein after subsequent time. A numerical example is given to illustrate the effectiveness of the proposed approach.