Stabilization on null controllable region of delta operator systems subject to actuator saturation

This paper focuses on stabilization on null controllable region of delta operator systems subject to actuator saturation via constructing suitable controllers. Under a saturated linear feedback law, a set of stable equilibrium points is obtained for the delta operator system with actuator saturation. A comprehensive controller is given to show global stabilization of the delta operator system. Thereby, semi‐global stabilization of the delta operator system is also achieved. For higher‐order systems with no more than two unstable exponentially poles, a new feedback law is constructed to achieve semi‐global stabilization on the null controllable region. Finally, three examples are given to illustrate the effectiveness of the proposed techniques. Copyright © 2016 John Wiley & Sons, Ltd.     

Output regulation for linear delta operator systems subject to actuator saturation

In this paper, output regulation for linear delta operator systems subject to actuator saturation is investigated by state feedback. The relation between the regulatable regions and the null controllable region is described in this paper. A set of all initial conditions of a plant and a exosystem is called asymptotically regulatable region for which output regulation is possible. An asymptotically regulatable region is characterized according to a null controllable region of an anti‐stable subsystem of the plant. Feedback laws are constructed to solve the problems on output regulation. A numerical example is given to illustrate the effectiveness and potential for the developed techniques. Copyright © 2016 John Wiley & Sons, Ltd.     

Quantized stabilization of networked control systems with actuator saturation

In this paper, we investigate the problems of stabilization of networked control systems with quantization and actuator saturation via delta operator approach. The definition of the domain of attraction for delta operator systems is introduced to analyze the stochastic stability of the closed‐loop networked control systems. The quantizer is a uniform one with arbitrary quantization regions, and the packet dropout process is modeled as a Bernoulli process. On the basis of the zoom strategy and Lyapunov theory in delta domain, sufficient conditions are given for the closed‐loop delta operator systems to be mean square stable, and the feedback controllers are designed to ensure the stability of networked control systems. A single link direct joint driven manipulator model is presented to show the effectiveness of the main results. Copyright © 2016 John Wiley & Sons, Ltd.     

区间Delta算子系统的鲁棒性分析与控制

研究Delta算子描述的区间系统的鲁棒稳定分析与鲁棒综合设计问题，在给出区间系统的一种等价描述后，利用Delta域的Lyapunov稳定性理论，提出了区间Delta算子系统鲁棒稳定的充分条件及状态反馈控制设计方法，所得结论可以将连续区间系统与离散区间系统的有关结果纳入到Delta算子系统的统一框架中。     

Maximal controllability of input constrained unstable systems by the addition of implicit constraints

The null controllable set of a system is the largest set of states that can be controlled to the origin. Control systems that have a region of attraction equal to the null controllable set are said to be maximally controllable closed-loop systems. In the case of open-loop unstable plants with amplitude constrained control it is well known that the null controllable set does not cover the entire state-space. Further the combination of input constraints and unstable system dynamics results in a set of state constraints which we call implicit constraints. It is shown that the simple inclusion of implicit constraints in a controller formulation results in a controller that achieves maximal controllability for a class of open-loop unstable systems.     

Semi-global stabilization with guaranteed regional performance of linear systems subject to actuator saturation

For a linear system under a given saturated linear feedback, we propose feedback laws that achieve semi-global stabilization on the null controllable region while preserving the performance of the original feedback law in a fixed region. Here by semi-global stabilization on the null controllable region we mean the design of feedback laws that result in a domain of attraction that includes any a priori given compact subset of the null controllable region. Our design guarantees that the region on which the original performance is preserved would not shrink as the domain of attraction is enlarged by appropriately adjusting the feedback laws. Both continuous-time and discrete-time systems will be considered.     

Analysis and design of delta operator systems with nested actuator saturation

In this paper, the problem of estimating the domain of attraction is considered for delta operator systems subject to nested actuator saturation. A set invariance condition is established for the delta operator system with nested actuator saturation in terms of auxiliary feedback matrices. Based on the set invariance condition, an optimisation approach is proposed to estimate the domain of attraction for the delta operator system. Thereby, the partial results of nested actuator saturation for both continuous-time systems and discrete-time systems are extended to delta operator system framework. A numerical example is provided to illustrate the effectiveness of the proposed design techniques.     

Delta算子时滞系统的可靠D--镇定

研究同时含有执行器故障和传感器故障的Delta算子时滞系统的鲁棒可靠D-镇定问题.利用矩阵特征值理论和线性矩阵不等式方法,给出了Delta算子时滞系统D-稳定的充分条件,进而,针对同时含有执行器故障和传感器故障的Delta算子范数有界参数不确定时滞系统,设计鲁棒可靠D-镇定状态反馈控制器,使得对于所有容许的不确定性、执行器故障和传感器故障,Delta算子闭环时滞系统的极点均落在复平面指定圆盘区域内.最后,通过数值算例验证了控制器设计方法的可行性和有效性.     

Global stabilization of linear systems by bounded controls with guaranteed poles

The global stabilization of asymptotically null controllable linear systems by bounded control is considered. A nested type saturation control law is proposed which is a generalization of the existing results reported in the literature. The primary characteristic of this modified control law is that more design parameters, which are the closed-loop eigenvalues when the system is operating in linear form, are introduced and which can be well designed to achieve better system performance. Using this law, the pole locations of the closed-loop systems depending on a linear trans- formation can be placed arbitrarily within certain areas. Numerical example shows that the performance of the closed-loop system under this control law can be significantly improved if the free parameters are properly chosen.     

Equivalence of input-output stability and exponential stability for infinite-dimensional systems

For a wide class of infinite-dimensional linear systems it is shown that if the state-space realization is exponentially stabilizable and detectable then exponential stability is equivalent to input-output stability of the transfer function. Exponential stabilizability (or detectability) is a strong assumption as it implies that the system operator satisfies the spectrum decomposition assumption and has finitely many unstable eigenvalues of finite multiplicity. In addition, the finite-dimensional unstable projection of the system is controllable (or observable).     

On controllability of diagonal systems with one-dimensional input space

This paper deals with diagonal systems on a Hilbert state space with a one-dimensional input space and a (possibly unbounded) control operator. A priori it is not assumed that the input operator is admissible. Necessary and sufficient conditions for different notions of controllability such as null-controllability, exact controllability and approximate controllability are presented. These conditions, which are given in terms of the eigenvalues of the diagonal operator and in terms of the control operator, are linked with the theory of interpolation in Hardy spaces.     

Finite spectrum assignment and observer for multivariable systems with commensurate delays

This paper is concerned with control of multivariable systems with commensurate delays. The purpose of this paper is to enlarge the class of finite spectrum assignable systems to spectrally controllable multivariable systems with commensurate delays. By overcoming an infinite number of eigenvalues which are contained in the system and make control very complex, it is proved that if the system is spectrally controllable, there is a delayed feedback matrix such that the closed-loop system is spectrally controllable through a single input. Combining this result with previous ones about single-input systems, it is verified that spectral controllability is equivalent to finite spectrum assignability for multivariable systems with commensurate delays. An observer for the system with delayed outputs is presented. By using these results, the multivariable system can be regulated as desired without preliminary knowledge of open-loop eigenvalues and a stability test of transcendental functions whenever the system is spectrally controllable and spectrally observable.     

Constrained control Lyapunov function based model predictive control design

This work considers linear systems with input constraints with the objective of designing a controller that guarantees stability from all initial conditions in the null‐controllable region (the set of initial conditions from where the system can be stabilized). To this end, a recently developed procedure for construction of constrained control Lyapunov functions is utilized within a Lyapunov‐based model predictive controller coupled with an auxiliary control design to achieve stabilization from all initial conditions in the null‐controllable region. Illustrative simulation results as well as an application to a nonlinear chemical process example is presented to demonstrate the efficacy of the results.Copyright © 2012 John Wiley & Sons, Ltd.     

Overall convergence rate of delta operator systems subject to actuator saturation

In this paper, overall convergence rate is considered for a delta operator system with actuator saturation. A saturation feedback law is presented for the delta operator system to obtain a desired overall convergence rate. Some properties on the overall convergence rate are revealed for time‐optimal actuator saturation delta operator systems. Limitations on the overall convergence rate are also investigated by proposed methods. An optimization problem is solved through a linear matrix inequality method to obtain the domain of attraction and overall convergence rate. Two numerical examples are provided to demonstrate the effectiveness of the proposed techniques. Copyright © 2017 John Wiley & Sons, Ltd.     

Null controllability of planar bimodal piecewise linear systems

This article investigates the null controllability of planar bimodal piecewise linear systems, which consist of two second order LTI systems separated by a line crossing through the origin. It is interesting to note that even when both subsystems are controllable in the classical sense, the whole piecewise linear system may be not null controllable. On the other hand, a piecewise linear system could be null controllable even when it has uncontrollable subsystems. First, the evolution directions from any non-origin state are studied from the geometric point of view, and it turns out that the directions usually span an open half space. Then, we derive an explicit and easily verifiable necessary and sufficient condition for a planar bimodal piecewise linear system to be null controllable. Finally, the article concludes with several numerical examples and discussions on the results and future work.     

Output regulation of general discrete‐time linear systems with saturation nonlinearities

This paper studies the classical problem of output regulation for linear discrete‐time systems subject to actuator saturation and extends the recent results on continuous‐time systems to discrete‐time systems. The asymptotically regulatable region, the set of all initial conditions of the plant and the exosystem for which the asymptotic output regulation is possible, is characterized in terms of the null controllable region of the anti‐stable subsystem of the plant. Feedback laws are constructed that achieve regulation on the asymptotically regulatable region. Copyright © 2002 John Wiley & Sons, Ltd.     

Synchronization in a network of identical continuous‐ or discrete‐time agents with unknown nonuniform constant input delay

This paper studies the synchronization problem for multiagent systems with identical continuous‐ or discrete‐time agents with unknown nonuniform constant input delays. The agents are connected via full‐ or partial‐state coupling. The agents are assumed to be asymptotically null controllable, ie, all eigenvalues are in the closed left‐half complex plane for continuous‐time agents or in the closed unit disc for discrete‐time agents. We derive an upper bound for the input delay tolerance, which explicitly depends on the agent dynamics. Moreover, for any unknown delay satisfying this upper bound, a low‐gain–based protocol design methodology is proposed without relying on exact knowledge of the network topology such that synchronization is achieved among agents for any network graph in a given set.     

Enlarging the domain of attraction and maximising convergence rate for delta operator systems with actuator saturation

In this paper, we present some new approaches to improve the feedback property of delta operator systems with actuator saturation. Both enlarging the domain of attraction and maximising the convergence rate are the desired feedback properties. The lifting technique is used to enlarge the domain of attraction for the delta operator systems subject to actuator saturation. The maximisation of convergence rate is realised by designing control gain inside a given ellipsoid. A necessary and sufficient condition is proposed for the contractive invariance of the given ellipsoid. Simulation results are provided to demonstrate the effectiveness of the developed techniques.     

Stability analysis for delta operator systems subject to state saturation

In this paper, we investigate the problem of stability analysis for linear delta operator systems subject to state saturation. Both full state saturation and partial state saturation are investigated for the delta operator systems. Two equivalent necessary and sufficient conditions are identified such that the system with full state saturation is globally asymptotically stable. Based on the sufficient conditions, an iterative algorithm is proposed for testing global asymptotic stability of the system with full state saturation. A new globally asymptotically stable condition is also proposed for the partial state saturation system. Two numerical examples on a ball and beam model are given to show the effectiveness of the proposed method.