Global regulation of a class of feedforward and non-feedforward nonlinear systems with a delay in the input

Output feedback regulation of a chain of integrators with unknown time-varying delays in states and input

“…In Zhang et al (2013), the main integrators and the control input do not have delays and time-varying delays only exist in the nonlinearity part. For these obvious reasons, the results of Bekiaris-Liberis and Krstic (2010); Koo et al (2012); Ye (2011); Zhang et al (2013) are not applicable to our considered system.…”

“…These results have their own merits in achieving robust global stabilization, dealing with uncertain delays and high-order terms. However, the results of Bekiaris-Liberis and Krstic (2010), Koo et al (2012), Ye (2011) commonly deal with constant delays. In Zhang et al (2013), the main integrators and the control input do not have delays and time-varying delays only exist in the nonlinearity part.…”

“…A chain of integrators system can be viewed as a special case of feedforward systems or lower triangular systems and there have been several results on the control of feedforward systems with delays (Koo et al, 2012;Ye, 2011), and lower triangular systems with delays (Bekiaris-Liberis & Krstic, 2010;Zhang et al, 2013). These results have their own merits in achieving robust global stabilization, dealing with uncertain delays and high-order terms.…”

“…Time-varying delays problems in control systems have received much attention and currently remain as active research areas in control engineering field (Bekiaris-Liberis, Jankovic, & Krstic, 2012;Bekiaris-Liberis & Krstic, 2010Bresch-Pietri, Chauvbin, & Petit, 2012;Choi & Lim, 2006Gielen, Teel, & Lazar, 2013;Jankovic, 2010;Karafyllis, 2006;Koo, Choi, & Lim, 2012;Krstic, 2010;Lei & Lin, 2007;Lin & Fang, 2007;Polyakov, Efimov, Perruquetti, & Richard, 2013;Richard, 2003;Yakoubi & Chitour, 2007;Ye, 2011;Zhang, Liu, & Zhang, 2013;Zhou, 2014;Zhou, Duan, & Lin, 2010;Zhou, Li, Zheng, & Duan, 2012). In this paper, we consider a chain of integrators with unknown timevarying delays in both states and input aṡ…”

Global asymptotic stabilization of stochastic feedforward nonlinear systems with input time-delay

“…Bekiaris-Liberis and Krstić [2] designed a Lyapunov-based adaptive controller for linear feedforward systems with arbitrary initial estimates for the delays. Koo et al [8], Krstić [10], Mazenc et al [17], Zhang et al [29], respectively, considered more general feedforward nonlinear systems with a delay in the input by using different design and analysis methods. When feedforward systems with state and input time-delay, [26] investigated adaptive stabilization problem by taking a nested saturation feedback and a set of switching logics, [27] constructed the delay-independent feedback controllers based on the Lyapunov-Razumikhin theorem and LyapunovKrasovskii theorem, [28] studied global strong stabilization for high-order feedforward systems by adopting a dynamic low-gain control scheme.…”