Global stabilisation for a class of more general high-order time-delay nonlinear systems by output feedback

This paper addresses the problem of global stabilisation by output feedback for a class of high-order time-delay nonlinear systems with more general uncertainties, which cover both high-order and low-order nonlinearities. By introducing sign function and necessarily modifying the homogeneous domination approach, an output feedback controller is successfully constructed to guarantee the global asymptotic stability of the resulting closed-loop system. Due to the versatility of the homogeneous domination approach and homogeneous properties, the proposed method is also utilised to the control design of upper-triangular systems.     

具有未知输出函数的非线性系统全局输出反馈控制

研究了一类具有未知输出函数的非线性系统全局输出反馈控制问题．由于输出函数未知,传统的观测器将无法实现．为解决这个问题,首先设计了一个与输出函数无关的状态补偿器,使得标称线性系统全局渐近稳定．然后,应用齐次控制方法通过适当选择增益参数,使得不确定非线性系统在有限时间内全局渐近稳定．数值算例表明该算法的有效性．     

Global sampled-data output feedback stabilisation for a class of nonlinear systems with unknown output function

This paper discusses the problem of global sampled-data output feedback stabilisation for a class of nonlinear systems whose output function is unknown. A systematic design scheme is developed to construct a linear output feedback control law in sampled-data form. An explicit formula for the maximum allowable sampling period is computed to guarantee global stability of the uncertain nonlinear systems under the proposed controller with appropriate gains. Two examples are given to demonstrate the effectiveness of the proposed design procedure.     

Global output feedback control of nonlinear time-delay systems with input matching uncertainty and unknown output function

This paper studies the problem of global output feedback control for nonlinear time-delay systems with input matching uncertainty and the unknown output function, whose nonlinearities are bounded by lower triangular linear unmeasured states multiplying the unknown constant, polynomial-of-output and polynomial-of-input growth rates. By constructing a new extended state observer and skillfully combining the dynamic gain method, backstepping method and Lyapunov–Krasovskii theorem, a delay-independent output feedback controller can be developed with only one dynamic gain. It is proved that all the signals of the closed-loop system are bounded, the states of the original system and the corresponding observer converge to zero, and the estimation of input matching uncertainty converges to its actual value. Two examples demonstrate the effectiveness of the control scheme.     

Global output feedback stabilisation for a class of upper triangular stochastic nonlinear systems

This paper investigates the problem of global output feedback stabilisation for a class of upper triangular stochastic nonlinear systems which are neither necessarily feedback linearisable nor affine in the control input. Based on the adding of a power integrator technique and homogeneous domination approach, an output feedback controller is explicitly constructed to ensure that the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability. A simulation example is provided to demonstrate the effectiveness of the design scheme.     

Output feedback stabilisation of high-order nonlinear feedforward time-delay systems

This paper studies the output feedback control problem for high-order nonlinear feedforward time-delay systems. Systems become more general due to both low-order and high-order in nonlinearities taking any value in certain intervals. By constructing the new Lyapunov–Krasovskii functional and reduced-order observer, based on the homogeneous domination theory, an output feedback controller is developed to guarantee high-order nonlinear feedforward time-delay systems globally asymptotically stable. A simulation example demonstrates the theoretical result.     

Global output feedback stabilisation of high-order nonlinear systems with multiple time-varying delays

This paper investigates the problem of global output feedback stabilisation for a class of high-order nonlinear systems with multiple time-varying delays. By using backstepping recursive technique and the homogeneous domination approach, a continuous output feedback controller is successfully designed, and the global asymptotic stability of the resulting closed-loop system is proven with the help of an appropriate Lyapunov– Krasovskii functional. Two simulation examples are given to illustrate the effectiveness of the proposed approach.     

Global finite-time stabilisation for a class of stochastic nonlinear systems by output feedback

In this paper, the problem of global finite-time stabilisation by output feedback is considered for a class of stochastic nonlinear systems. First, based on homogeneous systems theory and the adding a power integrator technique, a homogeneous reduced order observer and control law are constructed in a recursive manner for the nominal system. Then, the homogeneous domination approach is used to deal with the nonlinearities in drift and diffusion terms; it is shown that the proposed output-feedback control law can guarantee that the closed-loop system is global finite-time stable in probability. Finally, simulation examples are carried out to demonstrate the effectiveness of the proposed control scheme.     

Global output feedback stabilisation of stochastic high-order feedforward nonlinear systems with time-delay

This paper considers the problem of output feedback stabilisation for stochastic high-order feedforward nonlinear systems with time-varying delay. By using the homogeneous domination theory and solving several troublesome obstacles in the design and analysis, an output feedback controller is constructed to drive the closed-loop system globally asymptotically stable in probability.     

Output feedback stabilisation for nonlinear systems with unknown output function and control coefficients and its application

This paper solves the problem of output feedback stabilisation for nonlinear systems with unknown output function and control coefficients. Since output function is Lipschitz continuous but not necessary derivable, the maximal sector region of output function is given. As long as output function belongs to the sector, an output feedback controller can be designed to render the closed-loop system globally asymptotically stable. The effectiveness of controller is demonstrated by two examples.     

Feedback stabilisation of time-delay nonlinear systems with continuous time-varying output function

This paper investigates the problem of global output feedback stabilisation for a class of uncertain nonlinear systems, where output function is time-varying and continuous, and multiple time delays exist in system state at the same time. A double-domination method is used to capture time-varying measurement error and delayed states. The control strategy is presented based on the choice of Lyapunov–Krasovskii functionals and the construction of a novel state observer without using the information on the output function and nonlinearities. A simulation example is given to show the efficiency of the proposed control scheme.     

Finite-time output feedback stabilisation for a class of feedforward nonlinear systems with input saturation

This paper considers the problem of global finite-time stabilisation by output feedback for a class of feedforward (upper triangular) nonlinear systems with input saturation. Based on the finite-time stability theorem, and by skillfully using the homogeneous domination approach and the nested saturation technique, a saturated output feedback controller is successfully constructed, which renders the origin of the closed-loop system globally finite-time stable. In simulation studies, a numerical example is illustrated to show the effectiveness of the control scheme. Moreover, the design strategy is successfully applied to solve the saturated finite-time control problem for vertical wheel on rotating table.     

Finite-time output feedback stabilisation of chained-form systems with inputs saturation

This paper investigates the problem of finite-time stabilisation by output feedback for a class of non-holonomic systems in chained form with input saturation. Rigorous design procedure for saturated output feedback control is presented by using the homogeneous domination approach and the nested saturation technique. Together with a novel switching control strategy, the designed controller renders that the states of closed-loop system are regulated to zero in a finite time. A simulation example is provided to illustrate the effectiveness of the proposed approach.     

Global stabilisation of nonlinear time-delay systems by partial-state feedback

This paper studies the global stabilisation of a class of partial-state feedback nonlinear systems with time-varying delay. By adopting the dynamic gain-based design method and backstepping technique, a state-feedback controller is constructed with the help of appropriate Lyapunov–Krasovskii functional. It is proved that all the measurable states of the closed-loop systems converge to the origin, and a simulation example is given to verify the effectiveness of the proposed scheme.     

Global output feedback stabilization of upper-triangular nonlinear time-delay systems

In this paper,the problem of global output feedback stabilization for a class of upper-triangular nonlinear systems with time-varying time-delay in the state is considered.The uncertain nonlinearities are assumed to be higher-order in the unmeasurable states.Based on the extended homogeneous domination approach,using a low gain observer in combination with controller,the delay-independent output feedback controller makes closed-loop system globally asymptotically stable under a homogeneous growth condition.     

Global output feedback control for a class of nonlinear systems with unknown homogenous growth condition

This paper investigates the problem of global control for a class of nonlinear systems via output feedback. The system nonlinearities satisfy the homogenous growth condition with unknown growth rate. First, a homogenous observer is constructed for estimating the system state. Then, two novel dynamic gains are presented to deal with the unknown growth rate. Subsequently, by adding a power integrator technique, a dynamic output feedback controller is designed to guarantee that all the signals of the closed‐loop system are bounded and the system states globally converge to origin. Finally, an example is provided to illustrate the validity of the proposed control scheme.     

Global stabilisation for a class of upper-triangular nonlinear systems with unmodelled dynamics and time-delay

This paper considers the stabilisation control problem of upper-triangular nonlinear time-delay systems. One distinct characteristic of this work is that the systems contain unmodelled dynamics, unknown control coefficients and time-varying delay, which make the control design much more difficult. By modifying the homogeneous domination approach and introducing a gain-scaling method, a new controller is constructed such that all the states of the closed-loop systems are bounded and convergent to the origin. Simulation examples are given to illustrate the validity of the theory.     

A generalized homogeneous domination approach for global stabilization of inherently nonlinear systems via output feedback

In this paper, we introduce a generalized framework for global output feedback stabilization of a class of uncertain, inherently nonlinear systems of a particularly complex nature since their linearization around the equilibrium is not guaranteed to be either controllable or observable. Based on a new observer/controller construction and a homogeneous domination design, this framework not only unifies the existing output feedback stabilization results, but also leads to more general results which have been never achieved before, establishing this methodology as a universal tool for the global output feedback stabilization of inherently nonlinear systems. Copyright © 2006 John Wiley & Sons, Ltd.     

Decentralised adaptive output feedback stabilisation for stochastic time-delay systems via LaSalle-Yoshizawa-type theorem

This paper deals with the decentralised output feedback stabilisation problem for a class of large-scale stochastic time-delay nonlinear systems. A general theorem is firstly given to guarantee the global existence and uniqueness of the solution for stochastic time-delay systems. In addition, a stochastic version of the well-known LaSalle-Yoshizawa theorem with time-varying delay is initially proposed for the controller design and stability analysis. Then, for a class of large-scale stochastic systems with time-varying delays, totally decentralised adaptive delay-dependent controllers are designed by using K-filter and backstepping approach. Via LaSalle-Yoshizawa-type theorem and constructing a general Lyapunov function, it is shown that all signals in the closed-loop system are bounded almost surely and the solution is almost surely asymptotically stable. Finally, a simulation example is given to illustrate the effectiveness of the results of this paper.