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This article addresses the adaptive control problem for strict-feedback nonlinear time-varying systems with unknown control coefficients and external disturbances. To solve the problem of multiple unknown control coefficients, a new lemma based on a general class of Nussbaum functions rather than a specific Nussbaum function is proposed. By lumping all the time-varying parameters and control coefficients into an augmented time-varying vector, and combining the congelation of variables approach, a robust adaptive controller, without the restriction of the persistent excitation (PE) conditions, is constructed for the systems with external disturbances to guarantee the boundedness of all closed-loop variables. Then, by proper transformation, a novel adaptive control scheme is developed to achieve asymptotic stability for strict-feedback nonlinear time-varying systems without external disturbances. In addition, a tracking control method is acquired from the proposed adaptive control method. Finally, two simulations and an actual experiment demonstrate the applicability of the proposed schemes.

We focus on the problem of asymptotically mean-square stabilization in discrete-time stochastic systems that exhibit plant uncertainty, multiple input delays, and multiplicative noises. Our innovative contributions are described as follows. First, we employ a reduction method to transform the original model into a delay-free auxiliary system, and establish an equivalent proposition for stabilization based on this reformulation. On the basis of the reformulated model, we propose two stabilization criteria for the uncertainty-free case, including both Lyapunov-type and Riccati-type criteria. More generally, we extend the stabilization result to the uncertain model, and propose a necessary and sufficient stabilization criterion utilizing matrix homogeneous polynomials. Finally, we explore the existence and uniqueness of a delay margin under certain structural restrictions, and provide a closed-form representation of this margin.

In this article, the output feedback control design problem for a class of strict-feedback nonlinear systems with unknown state time-varying delays is addressed. Two output feedback control schemes are considered which are based on full-order and reduced-order observer, respectively. Lyapunov–Krasovskii functionals with static gain are used to develop novel memoryless control strategies. The above work ensures that all the signals in the closed-loop system are bounded and the system is asymptotically stable. Finally, two simulation examples illustrate the effectiveness of the two control schemes we proposed.