Class Of Lower-triangular Nonlinear Systems Research Articles

Global Regulation by Integral Feedback for Lower-Triangular Nonlinear Systems with Actuator Failures and Limited Delays

This paper studies the global asymptotic regulation problem for a class of lower-triangular nonlinear systems with actuator failures and limited delays. New integral controllers consisting of an integral dynamic are constructed to make all system states bounded and asymptotically convergent to zero. First, an integral dynamic is constructed and a novel state transformation is introduced, which ensures that the involved systems with actuator failures are converted into a class of auxiliary nonlinear systems without actuator failures. Second, by introducing the static high-gain technique, the problem of designing integral controllers for auxiliary nonlinear systems is converted into that of designing the gain parameter and determining the limit of the actuator delay. At last, with the help of the Lyapunov stability theorem, the gain parameter and the limit of the actuator delay are determined, and the stabilization of the auxiliary nonlinear systems yields the global asymptotic regulation of the involved systems. A physical system example is given to demonstrate the effectiveness of the proposed integral controllers.

Global stabilization of lower-triangular nonlinear systems with delayed input and delayed state

This paper addresses the problem of the global state feedback stabilization for a class of lower-triangular nonlinear systems whose states and input are perturbed by time-delay simultaneously. Quite different from upper-triangular systems, the presence of delayed input leads to the serious dependency of the stabilizer upon the size of the delays and the failed compensation of delayed states in such situation. The remarkable feature of the proposed method lies in the fact that it makes possible to achieve the stabilizing controller with the help of a simple inductive design and an integral Lyapunov function. Finally, theoretical results are illustrated and supported by the simulation.

Semi-Global Finite-Time Output-Feedback Stabilization With an Application to Robotics

The continuous finite-time stabilization of a broad class of lower-triangular nonlinear systems using output feedback is studied in this paper. The nonlinearities are only assumed to be Holder continuous. A constructive, continuous, finite-time, output-feedback stabilizer design is proposed based on a finite-time observer. Rigorous finite-time stability analysis is carried out for the closed-loop observer-controller system. The proposed design method is applied to a single-link robotic manipulator coupled to a dc motor.

Global Exponential/Finite-Time Stability of Nonlinear Adaptive Switching Systems With Applications in Controlling Systems With Unknown Control Direction

This paper focuses on the stability analysis and control of adaptive switching systems by establishing Lyapunov-based logic switching rules. Through considering performance-index-based adaptive switching control under a general framework, sufficient conditions are proposed and proved to ensure global generalized exponential stability and global finite-time stability. By taking these conditions as guidelines for designing control laws and logic switching rules, we explore their applications in controlling a class of lower-triangular nonlinear systems with an unknown control direction.

Finite-time output feedback stabilization of lower-triangular nonlinear systems

Abstract The finite-time stabilization of a general class of lower-triangular nonlinear systems using output feedback is addressed in this paper. The system nonlinearities are only required to be Holder continuous with output-dependent Holder coefficients. A new constructive output-feedback, finite-time controller design is proposed based on a finite-time observer. Rigorous finite-time stability analysis is given for the closed-loop observer–controller system. A practical example of controlling a robotic model is adopted to illustrate the proposed method.

Event‐triggered adaptive control for a class of non‐linear systems with multiple unknown control directions

This study investigates the event-triggered adaptive switching stabilisation problem for a class of lower-triangular non-linear systems with multiple unknown control directions. A novel Lyapunov-based event-triggered adaptive switching control rule is proposed to implement the stability of the closed-loop system. Moreover, a unified time sequence is introduced by combining two time sequences which are generated from such a control rule. The designed event-triggered adaptive switching controller not only ensures the closed-loop systems is globally generalised exponentially stable but also excludes the Zeno behaviour under the triggering condition. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed control strategy.

A semi-global finite-time convergent observer for a class of nonlinear systems with bounded trajectories

This paper considers the problem of designing finite-time convergent observers for a class of lower-triangular nonlinear systems with bounded solution trajectories. Using the homogeneous domination approach, we construct an observer with homogeneous structure and saturation design, whose states will converge to the real states in a finite time by adjusting the observer gain. Several application examples of this finite-time convergent observer are discussed in this paper.