Bandyopadhyay B., Janardhanan S. Discrete-time Sliding Mode Control. A Multirate Output Feedback Approach

Springer, 2006. — 160.Sliding mode control is a simple and yet robust control technique. In case of sliding mode control, the system states are made to confine to a selected subset of the state space so as to achieve some desirable dynamics. Traditionally, a relay-based control has been used for this purpose and had its roots in the variable structure system philosophy. Developed in the erstwhile Soviet Union, the concept was pioneered by Vadim Utkin.
With the increasing use of computers and discrete-time samplers in controller implementation in the recent past, discrete-time systems and computer based control have become topics that have a lot of potential in them. This had opened up the field of sliding mode control of discrete-time systems. Many researchers; W. B. Gao, E. Misawa, A. Bartoszewicz, K. Furuta, C. Milosavljevic, to cite a few had worked in this field. However, much of the work had been concentrated on state feedback based control. But, it is of common knowledge that only the system output is available for the controller design. More often than not, the system output is not coincident with the system state. This leads to the requirement of output feedback based sliding mode control strategies.
The existing literature on output feedback sliding mode control is either very restrictive, by being applicable to only a specific class of systems, even when one looks at the control of LTI systems alone. A wider class of systems can be controlled, if one adopts dynamic sliding mode controllers. However, the system complexity is increased in the process.
This is the motivation of this monograph: An output feedback sliding mode control philosophy which can be applied to almost all controllable and observable systems, while at the same time being simple enough as not to tax the computer too much. We found the answer in the synergy of the multirate output sampling concept and the concept of discrete-time sliding mode control.Switching Function based Multirate Output Feedback Sliding Mode Control
Multirate Output Feedback based Discrete-time Sliding Mode in LTI Systems with Uncertainty
Multirate Output Feedback based Discrete-timeQuasi-Sliding Mode Control of Time-Delay Systems
Multirate Output Feedback Sliding Mode for Special Classes of Systems
Discrete-time Terminal Sliding Mode: Concept
Applications of Multirate Output Feedback Discrete-time Sliding Mode Control