Design of sliding mode control for neutral delay systems with perturbation in control channels

Abstract

SUMMARYThis paper considers the problem of sliding mode control for a class of uncertain neutral delay systems. There are uncertainties not only in the state matrices, but also in the control matrix that results from perturbation in the control channels. By means of a sliding surface dependent on both the current states and delayed states, a sliding mode controller is designed such that the asymptotic stability of closed-loop systems can be ensured. The design of both the sliding surface and the sliding mode controller can be obtained via convex optimization. It is shown that the state trajectories are driven onto the specified sliding surface in finite time and remain there for subsequent time. Finally, a numerical simulation example is provided.

Decentralised sliding mode control for nonlinear interconnected systems in the regular form

“…In [8], it is shown that the sliding mode approach can be used to deal with systems in the presence of unmatched uncertainty. Methods proposed by Niu in [9] and [10] also show the strong robustness of sliding mode control for uncertain systems. Therefore, many researchers have tried to develop a decentralised sliding mode control strategy for large scale systems in the presence of uncertainties and interconnections.…”

“…Compared with existing work, e.g. see [9], [10], [19], the uncertainties in the input distribution are nonlinear instead of linear. It is emphasised that the uncertainties φ i (·) are not required to be matched, and only g…”

“…In [9] and [10], sliding mode control design is proposed for systems with uncertainties in the control matrix. However, the uncertainties in [9], [10] are assumed to have a particular structure, for example, the uncertainty is required to lie in the range of the control input distribution matrix. In most previous work, the nominal part of the system is usually assumed to be linear, which limits the application of the obtained results.…”

Robust H -infinity control for a class of neutral-type systems via sliding mode observer

“…In the past decades, SMC has proven to be an effective robust control strategy for incompletely modeled or uncertain systems, to mention a few [19][20][21][22][23][24][25][26][27][28][29]. Among them, the SMC for a class of NTSTD with uncertainties in both the state matrices and the input matrix were considered in [26,27], which gave sufficient conditions in terms of LMIs such that the closed-loop system is guaranteed to be asymptotically stable, respectively. Based on the neuralnetwork approximation approach, a new SMC scheme was put forward for uncertain NTSTD with unknown nonlinearity that might not satisfy the norm-bounded condition in [28].…”

Observer-Based $$H_\infty $$ H ∞ Sliding Mode Controller Design for Uncertain Stochastic Singular Time-Delay Systems

“…Sliding mode control (SMC), due to its attractive features such as fast response and good transient response, insensitivity to variations in system parameters and external disturbances, has become an effective robust control approach for a wide variety of practical engineering systems such as robot manipulators, aircraft, underwater vehicles, spacecraft, flexible space structures, electrical motors, power systems and automotive engines [3,20,32]. Many results have been reported on sliding mode control for different kinds of control systems, including stochastic systems [2,[16][17][18], uncertain systems [10,21,23,26,29], time-delay systems [15,17,23,25,26,31], Markovian jump systems [2,9,11,16,17,24,25] and singular systems [5][6][7]12,14,[22][23][24][25]31]. Wu and Ho D.W.C [22] studied SMC of singular stochastic hybrid systems.…”