State-Feedback Stabilization of Stochastic Non-holonomic Systems (SNSs) Under Arbitrary Switchings with Time-Varying Delays

Adaptive state-feedback stabilization of stochastic nonholonomic systems with an unknown time-varying delay and perturbations

“…System (3) is more general than some existing systems such as (Du et al 2015a; Gao et al 2011; Wang and Wei, 2007; Wang and Zhu 2018; Zhang et al 2012) in which d ( t ) = 0 . It should be pointed out that in Qin and Min (2018), the time-delay terms of systems are required to satisfy d i ≤ δ , for a known positive constant δ , and in Wu et al (2019), the time-delay terms of systems are required to satisfy τ · ( t ) ≤ η < 1 . From both theoretical and practical points of view, it is too restrictive to require a system to satisfy such delay restriction. Without imposing any assumptions on the time-varying delay, this paper largely generalizes the results in recent works on stochastic nonholonomic systems with time delay.…”

“…They obtained the adaptive state-feedback controller at the expense of delay-dependent nonlinear diffusion terms and constrained time-delay assumption, that is, d i ≤ δ for a known positive constant δ . Wu et al (2019) investigated state-feedback stabilization of stochastic nonholonomic systems under arbitrary switching with time-varying delays. However, the time-delay terms of systems are required to satisfy τ · ( t ) ≤ η < 1 . From both theoretical and practical points of view, it is too restrictive to require a system to satisfy such delay restriction.…”

State‐Feedback Stabilization of Stochastic Nonholonomic Systems with an Unknown Time‐Varying Delay

“…However, the aforementioned contributions have not taken into account the effect of time delay on the systems. e research of time delay systems has been received widespread attentions [15][16][17][18][19][20][21][22][23][24][25]. One reason is that the timedelay phenomenon frequently arises and is inevitable in many practical systems, such as chemical engineering systems, communication systems, and mechanical systems.…”

“…Qin and Min [22] studied the adaptive stabilization problem for a class of stochastic nonholonomic systems with time delays. is work gave the adaptive statefeedback control at the expense of delay-dependent nonlinear diffusion terms and time-delay assumption, i.e., d i ≤ δ for a known positive constant δ. Wu et al [23] studied statefeedback stabilization of stochastic nonholonomic systems under arbitrary switchings with time-varying delays. But the time-delay terms of stochastic nonholonomic systems is required to satisfy _ d(t) ≤ η < 1.…”