Robust quantized output feedback control for uncertain discrete time‐delay systems with saturation nonlinearity

This paper is concerned with robust quantized output feedback control problems for uncertain discrete‐time systems with time‐varying delay and saturation nonlinearity. It is assumed that the quantizer is of the saturating type. A new framework for the local boundedness stabilization of quantized feedback systems is developed. Attention is focused on finding a quantized static output feedback controller such that all trajectories of the resulting closed‐loop system starting from an admissible initial basin converge to a bounded region strictly within the initial basin. A quantized feedback controller is proposed, which comprises output feedback and the exogenous signal parts. Simulation examples are given to illustrate the effectiveness and advantage of the proposed methods. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust control of uncertain systems with polynomial nonlinearity by output feedback

The problem of global robust stabilization by output feedback is investigated for two classes of uncertain systems with polynomial nonlinearity—one is with controllable/observable linearization and the other is not. The uncertainties in the systems are assumed to be dominated by both lower‐ and higher‐order nonlinearities multiplying by an output‐dependent growth rate. There are two ingredients in this study. One is to exploit the idea of how to handle polynomial growth conditions via homogeneity and domination without introducing an observer gain updated law. The other is the development of a recursive design algorithm for the construction of reduced‐order observers, which is not only interesting in its own right but also has a valid counterpart, capable of dealing with strongly nonlinear systems, even lack of uniform observability and smooth stabilizability. Copyright © 2008 John Wiley & Sons, Ltd.     

Output feedback stabilisation for uncertain nonlinear time-delay systems subject to input constraints

Robust stabilisation of a class of imperfectly known systems with time-varying time-delays via output feedback is investigated. The systems addressed are composed of a nonlinear nominal system influenced by nonlinear perturbations which may be time-, state-, delayed state- and/or input-dependent. The output of the system is modelled by a nonlinear function, which may depend on the delayed states, and inputs, together with a feed-through term. Using bounding information on the perturbations, in terms of specified growth conditions, classes of unconstrained and constrained output feedback controllers are designed in order to guarantee a prescribed stability property for the closed-loop systems, provided appropriate stability criteria hold. Two stability criteria are given: one in terms of a linear matrix inequality (LMI) and the other is algebraic in nature, obtained using a Ger?gorin Theorem.     

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

This article considers the problem of global finite-time stabilisation by output feedback for a class of nonlinear systems comprised of a chain of power integrators perturbed by an uncertain vector field. To solve the problem, we first construct a homogeneous observer and controller in a recursive way for the nominal system without the perturbing nonlinearities. Then, using the homogeneous domination approach, we scale the homogeneous observer and controller with an appropriate choice of gain to render the uncertain nonlinear system globally finite-time stable. Due to the use of a reduced-order observer, the proposed output feedback controller is applicable to those systems with unknown gains associated with the power integrators.     

Exponential passivity for output feedback stabilisation of nonlinear uncertain systems

In this article, we address the problem of stabilisation by output feedback for a class of uncertain systems. We consider uncertain systems with a nominal part which is affine in the control and an uncertain part which is norm bounded by a known function. We propose an output feedback such that the closed loop system is globally exponentially stable.     

Stabilization of a chain of integrators with an unknown delay in the input by adaptive output feedback

In this note, we consider a stabilization problem of a chain of integrators with an unknown delay in the input. We propose an adaptive output feedback control scheme in which the delay-related low-gain parameter is tuned online by utilizing the integral value of the input norm-bound. Thus, a priori knowledge on the delay is not required for controller design.     

Semi‐global output feedback control for nonlinear systems with uncertain time‐delay and output function

This paper considers semi‐global output feedback control for more general nonlinear systems with unknown time‐delay and output function whose derivative is unbounded from above. By introducing a new observer and using the backstepping design method and the Razumikhin stability theorem, an output feedback controller is constructed to achieve a semi‐global stability. Copyright © 2016 John Wiley & Sons, Ltd.     

Global finite-time output feedback stabilisation for a class of uncertain nontriangular nonlinear systems

This article addresses the problem of global finite-time output feedback stabilisation for a class of nonlinear systems in nontriangular form with an unknown output function. Since the output function is not precisely known, traditional observers based on the output is not implementable. We first design a state observer and use the observer states to construct a controller to globally stabilise the nominal system without the perturbing nonlinearities. Then, we apply the homogeneous domination approach to design a scaled homogeneous observer and controller with an appropriate choice of gain to render the nonlinear system globally finite-time stable.     

Robust adaptive tracking of uncertain nonlinear systems by output feedback

We investigate the problem of robust adaptive tracking by output feedback for a class of uncertain nonlinear systems. Based on the high‐gain scaling technique and a new adaptive law, a linear‐like output feedback controller is constructed. Only one dynamic gain is designed, which makes the controller easier to implement. Furthermore, by modifying the update law, the adaptive controller is robust to bounded external disturbance and is able to guarantee the convergence of the output tracking error to an arbitrarily small residual set. A numerical example is used to illustrate the effectiveness of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

Global output feedback stabilisation of nonlinear systems with a unifying linear controller structure

We investigate the problem of global stabilisation by linear output feedback for a class of uncertain nonlinear systems with zero-dynamics. Compared with the previous works, new dilation-based assumptions are introduced that allow the system nonlinearities and its bounding functions to be coupled with all the states. The nonlinear systems of this paper can be considered as an extended form of some low triangular and feedforward systems. Dynamic gain scaling technique is applied to the controller design and stability analysis. It is proved that with a unifying linear controller structure and flexible adaptive laws for the observer gain, global stabilisation of the nonlinear systems can be achieved.     

A delay‐independent output feedback for linear systems with time‐varying input delay

It is well known that a delay‐dependent or delay‐independent truncated predictor feedback law stabilizes a general linear system in the presence of a certain amount of input delay. Results also exist on estimating the maximum delay bound that guarantees stability. In the face of a time‐varying or unknown delay, delay‐independent feedback laws are preferable over delay‐dependent feedback laws as the former provide robustness to the uncertainties in the delay. In the light of few results on the construction of delay‐independent output feedback laws for general linear systems with input delay, we present in this paper a delay‐independent observer–based output feedback law that stabilizes the system. Our design is based on the truncated predictor feedback design. We establish an estimate of the maximum allowable delay bound through the Razumikhin‐type stability analysis. An implication of the delay bound result reveals the capability of the proposed output feedback law in handling an arbitrarily large input delay in linear systems with all open‐loop poles at the origin or in the open left‐half plane. Compared with that of the delay‐dependent output feedback laws in the literature, this same level of stabilization result is not sacrificed by the absence of the prior knowledge of the delay.     

Robust and adaptive variable structure output feedback control of uncertain systems with input nonlinearity

This brief proposes a robust control algorithm for stabilization of a three-axis stabilized flexible spacecraft in the presence of parametric uncertainty, external disturbances and control input nonlinearity/dead-zone. The designed controller based on adaptive variable structure output feedback control satisfies the global reaching condition of sliding mode and ensures that the system state globally converges to the sliding mode. A modified version of the proposed control law is also designed for adapting the unknown upper bounds of the lumped uncertainties and perturbations. The stability of the system under the modified control law is established. Numerical simulations show that the precise attitude pointing and vibration suppression can be accomplished using the derived robust or adaptive controller.     

Delayed feedback control of uncertain systems with time-varying input delay

This paper is concerned with a delayed feedback control design for uncertain systems with time-varying input delay. Based on a reduction method, a new control design method is proposed by introducing some relaxation matrices and turning parameters, which can be chosen properly to lead to a less conservative result. A numerical example is given to show the effectiveness and less conservativeness of the method.     

Adaptive output feedback control of a class of uncertain nonlinear systems with unknown time delays

This article studies the adaptive output feedback control problem of a class of uncertain nonlinear systems with unknown time delays. The systems considered are dominated by a triangular system without zero dynamics satisfying linear growth in the unmeasurable states. The novelty of this article is that a universal-type adaptive output feedback controller is presented to time-delay systems, which can globally regulate all the states of the uncertain systems without knowing the growth rate. An illustrative example is provided to show the applicability of the developed control strategy.     

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.     

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.     

Robust stability analysis for uncertain delay systems with output feedback controller

A systematic approach is given in this paper for analyzing the robust stability of uncertain time-delay systems controlled by output feedback. By checking the eigenvalues of a Hamiltonian matrix, the stability of nominal systems can be examined first. Then, for the nominally stable uncertain systems with multiple time delays, a new method using structured singular value technique is proposed for finding a set of uncertain parameters within which the systems remain stable. Moreover, an illustrative example is given to show the usefulness of the proposed approach.     

Global stabilization of uncertain stochastic nonlinear time‐delay systems by output feedback

Constructive control techniques have been proposed for controlling strict feedback (lower triangular form) stochastic nonlinear systems with a time‐varying time delay in the state. The uncertain nonlinearities are assumed to be bounded by polynomial functions of the outputs multiplied by unmeasured states or delayed states. The delay‐independent output feedback controller making the closed‐loop system globally asymptotically stable is explicitly constructed by using a linear dynamic high‐gain observer in combination with a linear dynamic high‐gain controller. A simulation example is given to demonstrate the effectiveness of the proposed design procedure. Copyright © 2007 John Wiley & Sons, Ltd.     

一类不确定非线性系统的鲁棒输出反馈跟踪

讨论了一类严格反馈型不确定非线性系统的输出反馈跟踪问题. 所讨论的不确定性不满足线性增长条件. 先设计高增益观察器估计输出偏差的微分, 并将由此获得的信号的符号用于变结构观察器, 随后用backstepping过程设计输出反馈控制器. 得到的控制器可以保证闭环系统的所有信号都是有界的, 且跟踪误差可以任意地小.     

Adaptive output feedback regulation for a class of uncertain nonlinear systems

In this paper, the problem of global state regulation by output feedback is investigated for a class of uncertain nonlinear systems satisfying some relaxed upper‐triangular‐type condition. Using a linear dynamic gain observer with two dynamic gains and introducing two appropriate change of coordinates, we give a constructive design procedure for the linear‐like output feedback stabilizing controller. It is proved that the proposed controller globally regulates all the states of the uncertain system and maintains global boundedness of the closed‐loop system. An example is provided to demonstrate the effectiveness of the proposed design scheme. Copyright © 2014 John Wiley & Sons, Ltd.