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Nonlinear systems constantly suffer from time-varying delays, which cover slow delays and nonslow delays. The existing results were used to impose slow delay conditions and were used to study the control problems, but few pieces of research studies have discussed the case of systems with nonslow delay. In this work, we remove the slow time-delay condition and consider the nonlinear delayed system with complicated polynomial terms. By proposing a dynamic gain method and constructing a new Lyapunov–Razumikhin (L-R) function, we successfully construct a stable controller, which guarantees that the plant is globally asymptotically stable (GAS). An example is utilized to verify the raised control scheme.

In this work, the tracking control problem of nonlinear system which contains unknown parameters, multiple state delays, external disturbances and the dead-zone input is studied. By introducing a d...

This article investigates the robust stabilization problem for nonlinear time-delay systems with dead-zone input and complex dynamics. By flexibly using the inequality technique, the backstepping control method, and skillfully introducing a new Lyapunov–Krasovskii functional, we obtain a stable controller without using unmeasurable signals in the dynamic subsystem. The control system is guaranteed to be stable finally. Two simulation examples are given to verify the control strategy.

Summary This article studies the robust adaptive tracking control problem of nontriangular nonlinear systems that are affected by multiple state delays rather than the input‐delay. Different from t...

This paper considers the decentralized tracking control problem for stochastic high-order time-delay switched nonlinear systems. By designing a common Lyapunov–Krasovskii (L–K) functional and using a homogeneous domination approach, we construct an output tracking controller under arbitrary switching to guarantee that the tracking error can be tuned small enough in the mean-square sense while all states of the closed-loop system remain to be bounded in probability. Finally, a chemical reactor system with delayed recycle streams is used to verify the effectiveness of our developed theory.

This paper considers the global tracking control problem for a class of nonlinear systems. Compared with the existing results, one significant distinction of this work is that it allows the high-or...

This paper is concerned with the tracking control problem for a class of high-order nonlinear systems. Different from the related studies, the considered systems allow the existence of input dead-zone, external disturbances and polynomial growing conditions with time-varying delays. A new Lyapunov–Krasovskii functional is skillfully constructed and a robust output feedback tracking controller is designed by using a modified homogeneous domination method. It is guaranteed that all signals of the closed-loop system are bounded and the tracking error can converge to a compact domain which can be tuned sufficiently small. A simulation example is provided to show the validity of our control strategy.

This paper is concerned with the finite horizon linear quadratic (LQ) Pareto optimal control problem of stochastic singular systems. By means of the square completion technique, for the finite horizon LQ optimal control of stochastic singular systems, we establish a new kind of generalized differential Riccati equations (GDREs) and present the existence condition of the solution of the GDREs. Then, for the finite horizon LQ Pareto optimal control, it is shown that under the solvability of the corresponding GDREs, all Pareto candidates can be obtained by solving a weighting sum optimal control. Finally, an example is provided to show the effectiveness of our main results.

In this paper, we consider the robust stabilization control for a class of high-order nonlinear systems. Different from the existing work, the studied systems contain time-delay, input dead-zone and zero dynamics. By employing the modified homogeneous domination method, a delay-independent controller is presented such that all signals in the closed-loop system are bounded. A simulation example is studied to show the effectiveness of the method.

This paper studies the universal adaptive control for a class of stochastic nonlinear time-delay systems, which involve odd rational powers, multiple time-varying delays and parameter uncertainties. Since many new obstacles that have not been encountered should be carefully dealt with, the adaptive control problem remains challenging. A universal controller which employs the dynamic gain and the adaptive control strategy is firstly constructed to ensure that all signals of the closed-loop systems are bounded almost surely and the states of the considered systems converge to the origin almost surely. By proposing an extended method, another universal adaptive controller which removes the dynamic gain and reduces the order of the controller is also designed. A single-link robot system is considered to verify the effectiveness of the developed theory.

This paper considers the output tracking control problem for high-order stochastic time-delay nonlinear systems. By constructing a new Lyapunov–Krasovskii (L–K) functional and modifying the adding a power integrator method, an output tracking controller is well designed such that all signals of the closed-loop system are bounded in probability and the mean square of the tracking error can be adjusted as small as possible. The results are further extended to system with stochastic input-to-state stable (SISS) inverse dynamics. Simulation examples are provided to show the effectiveness of the theory.

This paper investigates the finite-time stabilization problem for a class of high-order uncertain nonlinear systems. The novel control strategy combining sign function with delicate adaptive technique can handle serious uncertainty and nonlinear growth rate. The convergent time can be adjusted arbitrarily by pre-assigning the design parameter. Finally, a numerical simulation example is given to show the effectiveness of the proposed design method.

This work studies the robust stabilization problem of non-triangular delayed nonlinear system. The considered system involves the uncertain dynamics, unknown control coefficient and time delay. By employing a novel Lyapunov-Krasovskii functional and using the backstepping method, we raise a robust controller to guarantee the states of the system bounded. An example is given to verify the validity of the strategy.

This paper is concerned with the adaptive stabilization problem of high-order stochastic nonlinear systems with time-varying delay. Indeed, there exist lots of deterministic results for the system without uncertainty and time delay. However, owing to the existence of time varying delay, unknown parameters and the relaxed nonlinear terms, it is not easy to choose an appropriate Lyapunov-Krasoviskii (L-K) functionals for control design. Via the modified method of adding a power integrator, an adaptive stabilization controller is constructed, which guarantees that the closed-loop system is globally asymptotically stable in probability. The effectiveness of the proposed approach is validated by a simulation example.