Abstract
ABSTRACTThe problem of robust control for a class of uncertain neutral stochastic systems (NSS) is investigated by utilising the sliding-mode observer (SMO) technique. This paper presents a novel observer and integral-type sliding-surface design, based on which a new sufficient condition guaranteeing the resultant sliding-mode dynamics (SMDs) to be mean-square exponentially stable with a prescribed level of performance is derived. Then, an adaptive reaching motion controller is synthesised to lead the system to the predesigned sliding surface in finite-time almost surely. Finally, two illustrative examples are exhibited to verify the validity and superiority of the developed scheme.
Highlights
Neutral systems, where the delays exist in both the system state and the state derivative, have been received great attention in the control community during the past decades, and arise in various applications (Hale, & Verduyn Lunel, 1993), e.g., the lossless transmission system, simultaneously
For the more general case where the control matrix B is perturbed by some factors, i.e., B(x, χ, t), where χ is an uncertain parameter vector (Hung, Gao, & Hung, 1993), the following uncertain neutral system is taken as example: x(t) − Dx(t − τ) = A(t)x(t) + Ad(t)x(t − d) + B(x, χ, t)u(t) + Gv(t), (1)
We recall the physical meaning of (2) is that all modeling uncertainties and disturbances enter the system through the control channel, i.e., the matched uncertainties in sliding mode control (SMC) theory (Hung et al, 1993)
Summary
Neutral systems, where the delays exist in both the system state and the state derivative, have been received great attention in the control community during the past decades, and arise in various applications (Hale, & Verduyn Lunel, 1993), e.g., the lossless transmission system, simultaneously. It should be mentioned that, the matched ones has been done for deterministic neutral systems, where the general method is that: Both the controller itself and a discontinuous output error injection term (or called the controller compensator) are required to design for rejecting the uncertainties and guaranteeing robust stability of the closed-loop systems. In such case, the associated problems including the sliding surface design will be more complicated to configure. L2[0, ∞) stands for the space of square integral vector functions over [0, ∞)
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