Global Stabilization of High-Order Time-Delay Nonlinear Systems under a Weaker Condition

Abstract

Under the weaker condition on the system growth, this paper further investigates the problem of global stabilization by state feedback for a class of high-order nonlinear systems with time-varying delays. By skillfully using the homogeneous domination approach, a continuous state feedback controller is successfully designed, which preserves the equilibrium at the origin and guarantees the global asymptotic stability of the resulting closed-loop system. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.

NN approach to state-feedback control of high-order non-linear time-delay systems with time-varying control coefficient

“…Compared with Gao et al (2013), Gao and Wu (2015a,b), Zhang et al (2014) and Zhang and Lin (2014), in which the homogeneous domination approach was used to somewhat relax the growth conditions, this paper can further weaken or even remove the growth conditions by adopting the RBF NN approximation approach.…”

“…Since time delays and control coefficients are common in many practical systems that may affect system stability, the design and investigation of non-linear time-delay systems with unknown control coefficients is of great importance. By combining the homogeneous domination approach with appropriate Lyapunov–Krasovskii functionals, Gao and Wu (2015a,b), Zhang et al (2014) and Zhang and Lin (2014) proposed different control schemes for time-delay systems in the absence of control coefficients. In Gao et al (2013), the authors explicitly constructed a state-feedback controller for a class of high-order non-linear systems with time delays and unknown control coefficients being bounded by two positive constants.…”

“…In Gao et al (2013), the authors explicitly constructed a state-feedback controller for a class of high-order non-linear systems with time delays and unknown control coefficients being bounded by two positive constants. Note that all the mentioned results (Gao et al, 2013; Gao and Wu, 2015a,b; Zhang et al, 2014; Zhang and Lin, 2014) still require the growth conditions with the value range of the degree of homogeneity being either a fixed point or on an interval even when using the homogeneous domination approach. This is somewhat restrictive from a practical and theoretical viewpoint.…”

Global output tracking by state feedback for high-order nonlinear systems with time-varying delays

“…However, due to there being no unified method being applicable to nonlinear control design, this problem has not been fully investigated and there are many significant problems which remain unsolved. In recent years, by using the Lyapunov-Krasovskii method to deal with the timedelay, control theory, and techniques for stabilization problem of time-delay nonlinear systems were greatly developed and advanced methods have been made; see, for instance, (Chai, 2013;Gao & Wu, 2015;Gao, Wu, & Yuan, 2016;Gao, Yuan, & Wu, 2013;Sun, Liu, & Xie, 2011;Sun, Xie, & Liu, 2013;Zhang, Lin, & Lin, 2017;Zhang, Zhang, & Gao, 2014) and reference therein. In the case when the nonlinearities contain time-delay, for the output tracking problems, some interesting results also have been obtained (Alimhan, Otsuka, Kalimoldayev, & Tasbolatuly, 2019;Jia, Xu, Chen, Li, & Zou, 2015;Jia, Xu, & Ma, 2016;Yan & Song, 2014).…”

Output Feedback Stabilization of High-Order Nonlinear Time-Delay Systems With Low-Order and High-Order Nonlinearities

“…achieved, see [8]- [10] and the reference therein. However, [8] only considered high-order nonlinearities, [9] only had an order in , [10] allowed low-order to be and high-order to take any value in .…”