Asymptotic Tracking Control for Uncertain Nonlinear Strict-Feedback Systems With Unknown Time-Varying Delays

Finite‐time tracking control for time‐delayed pure‐feedback systems with guaranteed performance

“…The strict condition for the nonlinear state delay term $$$ {h}_i\left(\cdotp \right) $$$ that the function $$$ {\rho}_{ij} $$$ needs to be known in most existing works 8–11 has been removed in Assumption 3 in this work. It is worth noting that in References 14,16,22, the prior knowledge of $$$ {\varrho}_{ij} $$$ is also not required; however, only constant but not time‐varying state time delays are considered in Reference 14, and only nonstrict‐feedback systems or strict‐feedback systems, respectively, but not pure feedback systems are considered in References 16,22. In this article, not only prior knowledge of $$$ {\varrho}_{ij} $$$ is not required, but also a more general non‐affine pure‐feedback system subject to unknown time‐varying state time delays is considered.…”

“…Numerous studies have employed LK and LR functions to investigate different classes of nonlinear systems, with a significant portion explicitly addressing constant state delays [8][9][10][11][12][13][14] or time-varying state delays. [15][16][17][18][19][20][21][22] However, the LR functions method necessitates strict adherence to stability conditions, which can result in conservative conclusions. Consequently, recent research has predominantly emphasized the adoption of the LK functions method.…”

“…Lyapunov–Krasovskii (LK) functions 6 and Lyapunov–Razumikhin (LR) functions 7 are widely recognized as common tools for stability analysis of systems with time delays. Numerous studies have employed LK and LR functions to investigate different classes of nonlinear systems, with a significant portion explicitly addressing constant state delays 8–14 or time‐varying state delays 15–22 . However, the LR functions method necessitates strict adherence to stability conditions, which can result in conservative conclusions.…”