Global sampled‐data output‐feedback stabilization for nonlinear systems with unknown measurement sensitivity

This paper investigates the problem of global output‐feedback stabilization by sampled‐data control for nonlinear systems with unknown measurement sensitivity. By employing the technique of output‐feedback domination, a sampled‐data output‐feedback control law together with a sampled‐data state observer is explicitly constructed. By an exquisite selection of both the domination gain and sampling period, the resultant control law is a globally asymptotic stabilizer even in the presence of unknown measurement sensitivity. The novelty of this paper is the development of a distinct approach which can tackle the problem of output‐feedback stabilization for the nonlinear systems with unknown measurement sensitivity.     

Global output feedback sampled‐data stabilization for upper‐triangular nonlinear systems with improved maximum allowable transmission delay

This paper addresses the problem of output feedback sampled‐data stabilization for upper‐triangular nonlinear systems with improved maximum allowable transmission delay. A class of hybrid systems are firstly introduced. The transmission delay may be larger than the sampling period. Then, sufficient conditions are proposed to guarantee global exponential stability of the hybrid systems. Based on these sufficient conditions and a linear continuous‐discrete observer, an output feedback control law is presented to globally exponentially stabilize the feedforward nonlinear system. The improved maximum allowable transmission delay is also given. The results are also extended to output feedback sampled‐data stabilization for lower‐triangular nonlinear systems. Finally, illustrative examples are used to verify the effectiveness of the proposed design methods. Copyright © 2016 John Wiley & Sons, Ltd.     

Almost Disturbance Decoupling for a Class of Nonlinear Systems Subject to Time‐Delays Via Sampled‐Data Output Feedback Control

This paper considers the problem of almost disturbance decoupling (ADD) via sampled‐data output feedback control for a class of uncertain nonlinear systems subject to time‐delays. Based on output feedback domination approach, a sampled‐data output feedback controller is designed to globally stabilize the system under a lower‐triangular linear growth condition. Gronwall‐Bellman‐like inequality and inductive method are introduced to estimate the state growth in the presence of time‐delays, uncertain nonlinearities and unknown disturbances. The proposed controller can attenuate the influence of disturbances on the output to an arbitrary degree in the L₂ gain sense. Finally, simulation results show the effectiveness of the control method.     

Global Output‐Feedback Stabilization for Stochastic Nonlinear Systems with Function Control Coefficients

This paper investigates the global output‐feedback stabilization for a class of stochastic nonlinear systems with function control coefficients. Notably, the systems in question possess control coefficients that are functions of output, rather than constants; hence, they are different from the existing literature on stochastic stabilization. To solve the control problem, an appropriate reduced‐order observer is introduced to reconstruct the unmeasured system states before a smooth output‐feedback controller is designed using the backstepping method, which guarantees that the closed‐loop system is globally asymptotically stable in probability. This paper combines the related results in the deterministic and stochastic setting and gives the first treatment on the global output‐feedback stabilization for the stochastic nonlinear systems with function control coefficients. A simulation example is given also to illustrate the effectiveness of the proposed approach.     

Global finite‐time stabilization for a class of high‐order switched nonlinear systems via sampled‐data control

This paper investigates the global finite‐time stabilization for a class of high‐order switched nonlinear systems via the sampled‐data output feedback control. Firstly, we design a continuous‐time output feedback controller for the nominal part via adding a power integrator technique. Based on the homogeneous theory, together with the Gronwall‐Bellman inequality, a sampled‐data output feedback controller is designed with suitable sampling periods to ensure that the closed‐loop system can be globally stabilized in finite time. In the meantime, the proposed control method can be extended to the switched nonlinear systems with an upper‐triangular growth condition. Finally, two examples are presented to illustrate the validity of the proposed control scheme.     

Output feedback stabilization for a general class of nonlinear systems via sampled‐data control

This paper considers global output feedback stabilization via sampled‐data control for a general class of nonlinear systems, which admit unknown control coefficients and nonderivable output function. A sector region of the output function is given by utilizing a technical lemma, and a sampled‐data controller is designed by combining a robust state stabilizer and a reduced‐order sampled‐data observer. By carefully choosing an appropriate sampling period, the proposed controller guarantees the globally asymptotical stability of the closed‐loop systems.     

Global output‐feedback stabilization for stochastic nonlinear systems: A double‐domination approach

This paper is concerned with global stabilization via output feedback for a class of stochastic nonlinear systems with time‐varying continuous output function. Under linear growth conditions, a new double‐domination method is proposed for the first time to construct an output‐feedback stabilizing controller. Different from the related results, the design of the observer is performed without using the information on the output function and nonlinearities. This paper also provides a viewpoint at the feedback stabilization to eliminate the continuous measurement error originating from inaccurate detection of system state. A simulation example is presented to demonstrate the effectiveness of control strategy.     

Almost disturbance decoupling for a class of nonlinear systems via sampled‐data output feedback control

This paper addresses the problem of almost disturbance decoupling (ADD) using sampled‐data output feedback control for a class of continuous‐time nonlinear systems. Under a lower‐triangular linear growth condition, a sampled‐data output feedback controller is constructed based on the output feedback domination approach, and a Gronwall–Bellman‐like inequality is established in the presence of disturbances. Even though a sampled‐data controller is employed for easy computer implementation, the proposed controller is still able to achieve ADD under the commonly used continuous‐time requirement, that is, the disturbances' effect on the output is attenuated to an arbitrary degree of accuracy in the L₂ gain sense. Copyright © 2015 John Wiley & Sons, Ltd.     

Sampled‐data output feedback stabilization for a class of switched stochastic nonlinear systems

This paper investigates a global sampled‐data output feedback stabilization problem for a class of switched stochastic nonlinear systems whose output and system mode are available only at the sampling instants. An observer is designed to estimate the unmeasurable state and thus a sampled‐data controller is constructed with the sampled estimated state. As a distinctive feature, a merging virtual switching signal is introduced to describe the asynchronous switching generated by detecting the system mode via a sampler. By choosing an appropriate piecewise Lyapunov function, it is proved that the proposed sampled‐data controller with allowable sampling period can stabilize the considered switched stochastic nonlinear systems under an average dwell‐time condition. Finally, two simulation results are presented to illustrate the effectiveness of the proposed method.     

Robust control of a family of uncertain nonminimum‐phase systems via continuous‐time and sampled‐data output feedback

The problem of global robust stabilization is studied by both continuous‐time and sampled‐data output feedback for a family of nonminimum‐phase nonlinear systems with uncertainty. The uncertain nonlinear system considered in this paper has an interconnect structure consisting of a driving system and a possibly unstable zero dynamics with uncertainty, ie, the uncertain driven system. Under a linear growth condition on the uncertain zero dynamics and a Lipschitz condition on the driving system, we show that it is possible to globally robustly stabilize the family of uncertain nonminimum‐phase systems by a single continuous‐time or a sampled‐data output feedback controller. The sampled‐data output feedback controller is designed by using the emulated versions of a continuous‐time observer and a state feedback controller, ie, by holding the input/output signals constant over each sampling interval. The design of either continuous‐time or sampled‐data output compensator uses only the information of the nominal system of the uncertain controlled plant. In the case of sampled‐data control, global robust stability of the hybrid closed‐loop system with uncertainty is established by means of a feedback domination method together with the robustness of the nominal closed‐loop system if the sampling time is small enough.     

Finite‐time stabilization for a class of stochastic low‐order nonlinear systems with unknown control coefficients

This paper addresses the problem of finite‐time stabilization for a class of low‐order stochastic upper‐triangular nonlinear systems corrupted by unknown control coefficients. Unlike the relevant schemes, the control strategy draws into a dominate gain to cope with the deteriorative effects of both uncertain nonlinearities and unknown control coefficients without using traditional adaptive compensation method. Then, a state feedback controller is constructed by the adding a power integrator method and modified homogeneous domination approach, to ensure the finite‐time stability of the closed‐loop system. Finally, the effectiveness of proposed control strategy has been demonstrated by a simulation example.     

Global output feedback stabilization of upper‐triangular nonlinear systems using a homogeneous domination approach

This paper addresses the problem of global output feedback stabilization for a class of upper‐triangular systems with perturbing nonlinearities that are higher‐order in the unmeasurable states. A new design method based on the homogeneous domination approach and finite‐time stabilization technique is developed, which leads to global output feedback stabilizers for the upper‐triangular nonlinear systems under a homogeneous growth condition. A new perspective shown in this paper is that the finite‐time stabilization, in addition to its faster convergence rate, can also be utilized to handle control problems that were previously unresolved under asymptotic stabilization. Copyright © 2006 John Wiley & Sons, Ltd.     

Continuous finite‐time state feedback stabilizers for some nonlinear stochastic systems

This paper is concerned with the problem of finite‐time stabilization for some nonlinear stochastic systems. Based on the stochastic Lyapunov theorem on finite‐time stability that has been established by the authors in the paper, it is proven that Euler‐type stochastic nonlinear systems can be finite‐time stabilized via a family of continuous feedback controllers. Using the technique of adding a power integrator, a continuous, global state feedback controller is constructed to stabilize in finite time a large class of two‐dimensional lower‐triangular stochastic nonlinear systems. Also, for a class of three‐dimensional lower‐triangular stochastic nonlinear systems, a recursive design scheme of finite‐time stabilization is given by developing the technique of adding a power integrator and constructing a continuous feedback controller. Finally, a simulation example is given to illustrate the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Output feedback control for a class of stochastic high‐order nonlinear systems with time‐varying delays

This paper discusses the problem of output feedback stabilization for a more general class of stochastic high‐order nonlinear systems with time‐varying delays. On the basis of a subtle homogeneous observer and controller construction, and the homogeneous domination approach, the closed‐loop system is globally asymptotically stable in probability, by choosing an appropriate Lyapunov–Krasovskii functional. An example is given to illustrate the effectiveness of the proposed design procedure. Copyright © 2013 John Wiley & Sons, Ltd.     

Global control of nonlinear systems with uncertain output function using homogeneous domination approach

This paper addresses the problem of using output feedback to globally control a class of nonlinear systems whose output functions are not precisely known. First, for the nominal linear system, we design a homogeneous state compensator without requiring precise information of the output function, and construct a nonlinear stabilizer with adjustable coefficients by using the generalized adding a power integrator technique. Then based on the homogeneous domination approach, a scaling gain is introduced into the proposed output feedback controller, which can be used by tuning the scaling gain to solve: (i) the problem of global output feedback stabilization for a class of upper‐triangular systems; and (ii) the problem of global practical output tracking for a class of lower‐triangular systems. Copyright © 2011 John Wiley & Sons, Ltd.     

Sampled‐data control of a class of uncertain switched nonlinear systems in nonstrict‐feedback form

This paper investigates the stabilization problem of sampled‐data output feedback for a class of uncertain switched nonlinear systems in nonstrict‐feedback form. An observer is designed to estimate the unmeasured states, and a sampled‐data controller is obtained by discretizing the virtual controller that is constructed via the dynamic surface control method. It is proved that the designed sampled‐data controller can render all states of the resulting closed‐loop system to converge to a neighborhood of the origin for the arbitrary switching signal, and an allowable sampling period is also given. Finally, 2 examples are presented to illustrate the effectiveness of the proposed method.     

Finite‐time output feedback stabilization of nonlinear high‐order feedforward systems

This paper considers the global finite‐time output feedback stabilization of a class of nonlinear high‐order feedforward systems. By using the homogeneous domination method together with adding a power integrator method and overcoming several troublesome obstacles in the design and analysis, a global finite‐time output feedback controller with reduced‐order observer is recursively designed to globally finite‐time stabilize nonlinear high‐order feedforward systems. Copyright © 2015 John Wiley & Sons, Ltd.     

State‐feedback stabilization for a class of stochastic time‐delay nonlinear systems

This paper investigates the problem of state‐feedback stabilization for a class of lower‐triangular stochastic time‐delay nonlinear systems without controllable linearization. By extending the adding‐a‐power‐integrator technique to the stochastic time‐delay systems, a state‐feedback controller is explicitly constructed such that the origin of closed‐loop system is globally asymptotically stable in probability. The main design difficulty is to deal with the uncontrollable linearization and the nonsmooth system perturbation, which, under some appropriate assumptions, can be solved by using the adding‐a‐power‐integrator technique. Two simulation examples are given to illustrate the effectiveness of the control algorithm proposed in this paper.Copyright © 2011 John Wiley & Sons, Ltd.     

Global Robust Stabilization via Sampled‐Data Output Feedback for Nonlinear Systems with Uncertain Measurement and Control Gains

This paper studies the problem of using a sampled‐data output feedback controller to globally stabilize a class of nonlinear systems with uncertain measurement and control gains. A reduced‐order observer and a linear output control law, both in the sampled‐data form, are designed without the precise knowledge of the measurement and control gains except for their bounds. The observer gains are chosen recursively in a delicate manner by utilizing the output feedback domination approach. The allowable sampling period is determined by estimating and restraining the growth of the system states under a zero‐order‐hold input with the help of the Gronwall–Bellman Inequality. A DC–DC buck power converter as a real‐life example will be shown by numerical simulations to demonstrate the effectiveness of the proposed control method.     

Robust output feedback stabilization of nonlinear systems with low‐order and high‐order nonlinearities

In this paper, we consider the problem of global output feedback stabilization for a class of nonlinear systems whose nonlinearities are assumed to be bounded by both low‐order and high‐order nonlinearities multiplied by a polynomial‐type output‐dependent growth rate. Instead of the previously proposed dual observer, based on the homogeneous domination approach, a new reduced‐order observer is constructed, which greatly simplifies the closed‐loop controller and is able to cover a more general class of nonlinear systems. Copyright © 2015 John Wiley & Sons, Ltd.