时滞不确定采样控制系统的鲁棒稳定性

本文给出了一种可定量分析采样控制系统的时滞鲁棒稳定性的方法.因为采样系统的对象是连续时间的,所以对象中的时滞也应该是按连续时间来处理.文中指出,一个整数倍时滞是稳定的采样系统,可能会因为有并不很大的连续时间时滞而失稳.定义了一个新的变量w(t),用来描述这个不确定连续时间时滞带来的动特性.将w(t)的反馈回路分成与时滞无关和有关的两个部分,并提出了一种用频率响应来确定是否存在由不确定时滞引起的周期解的方法.用修正z-变换法和仿真验证了这个由图解解析所求得的解.本方法既可用于采样系统,也可用于一般的连续时间系统.     

Robust sampled-data control with random missing data scenario

The problem of robust sampled-data control for uncertain dynamic systems in the presence of missing data has been investigated. By using stochastic variables with a Bernoulli distributed white sequence to model missing data, along with time-varying norm-bounded uncertainties, and the input delay approach for sampled-data systems, two models for the considered sampled-data control system are proposed as the consecutive missing data scenario. Moreover, when data are missing, the control signals are held as the last received data. Sufficient conditions for the existence of desired robust sampled-data controllers are presented in the form of a linear matrix inequality. A numerical example is given to illustrate the validity of the proposed methods and to compare the results between the two proposed models of the sampled-data control system.     

Robust stability evaluation of sampled-data control systems with a sector nonlinearity in a gain-phase plane

This paper describes a graphical evaluation of the robust stability in a frequency domain based on the results from our previous paper in which the extension of Popov's criterion to discrete-time systems was expressed in an explicit form. The control system described herein is a sampled-data control system with one time-invariant nonlinear element (sector nonlinearity) in the forward path. For the purpose of application to a computer-aided control system design (CACSD), we will present an evaluation method of the robust stability in connection with the size of sector nonlinearity and the gain margin on a gain-phase diagram (i.e. a modified Nichols chart). We will show two results as numerical examples: one where Aizerman's conjecture was approved, and one where it was not. Copyright © 1999 John Wiley & Sons Ltd.     

Indirect sampled-data control with sampling period adaptation

It is known that if a continuous-time feedback system is exponentially stable, then the corresponding sampled-data system obtained by sample-hold discretisation with constant sampling period is also exponentially stable, provided that the sampling period τ?>?0 is sufficiently small. In general, it is difficult to estimate how small the sampling period has to be in order to achieve the stability of the sampled-data system. In this article, we present an adaptive mechanism for adjusting the sampling period. This mechanism has the properties that, for every initial state, (i) the adaptation of the sampling period terminates after finitely many time steps and (ii) the state of the adaptive sampled-data system is integrable and converges to zero as time goes to infinity.     

基于分段连续Lyapunov函数的采样系统鲁棒保性能控制

针对不确定采样控制系统的鲁棒保性能控制问题,首先将采样系统描述为跳变线性系统,基于矩阵凸组合思想构造了分段连续Lyapunov函数,进而在线性矩阵不等式框架内给出了不确定采样系统鲁棒稳定的条件.针对范数有界参数不确定采样系统,提出了鲁棒保性能控制器设计的在线算法,在每个采样周期内通过求解一组线性矩阵不等式的可行解来构造出状态反馈增益矩阵.最后的仿真算例验证了所提设计方法的有效性.     

Robust reliable control design for networked control system with sampling communication

In this article, the problem of robust exponential stability and reliable stabilisation for a class of continuous-time networked control systems (NCSs) with a sample-data controller and unknown time-varying sampling rate is considered. The analysis is based on average dwell-time, Lyapunov–Krasovskii functional and linear matrix inequality (LMI) technique. The delay-dependent criteria are developed for ensuring the robust exponential stability of the considered NCSs. The obtained conditions are formulated in terms of LMIs that can easily be solved by using standard software packages. Furthermore, the result is extended to study the robust stabilisation for NCS with parameter uncertainties. A state feedback controller is constructed in terms of the solution to a set of LMIs, which guarantee the robust exponential stabilisation of NCS and the controller. Finally, numerical examples are presented to illustrate the effectiveness of the obtained results.     

Asymptotic stabilisation of a class of nonlinear systems via sampled-data output feedback control

This article considers sampled-data output feedback control of a class of nonlinear systems in output feedback form. The underlying continuous-time controller is designed based on backstepping technique, employing a linear dynamic filter, and globally asymptotically stabilises the system. Rigorous analysis shows that when implemented with a sampling and zero-order hold device, the sampled-data version of the continuous-time controller semi-globally asymptotically stabilises the original system, given that the sampling period is smaller than a specific value, which depends on the initial values and nonlinearity of the system. Simulation results of a physical system are included in the end.     

Decentralised output feedback for a class of nonlinear systems via quantised sampled-data control

We design a decentralised observer-based sampled-data controller with quantised output for a class of interconnected nonlinear systems. Instead of quantising the output directly, we quantise the sampled output to avoid sudden jump. It can be proved that by choosing suitable design parameters, global stability of the system is achieved. An example is given to illustrate the effectiveness of the proposed method.     

Robust reliable sampled-data control for switched systems with application to flight control

This paper addresses the robust reliable stabilisation problem for a class of uncertain switched systems with random delays and norm bounded uncertainties. The main aim of this paper is to obtain the reliable robust sampled-data control design which involves random time delay with an appropriate gain control matrix for achieving the robust exponential stabilisation for uncertain switched system against actuator failures. In particular, the involved delays are assumed to be randomly time-varying which obeys certain mutually uncorrelated Bernoulli distributed white noise sequences. By constructing an appropriate Lyapunov–Krasovskii functional (LKF) and employing an average-dwell time approach, a new set of criteria is derived for ensuring the robust exponential stability of the closed-loop switched system. More precisely, the Schur complement and Jensen's integral inequality are used in derivation of stabilisation criteria. By considering the relationship among the random time-varying delay and its lower and upper bounds, a new set of sufficient condition is established for the existence of reliable robust sampled-data control in terms of solution to linear matrix inequalities (LMIs). Finally, an illustrative example based on the F-18 aircraft model is provided to show the effectiveness of the proposed design procedures.     

Sampling-interval-dependent stability for linear sampled-data systems with non-uniform sampling

This paper is concerned with the sampling-interval-dependent stability of linear sampled-data systems with non-uniform sampling. A new Lyapunov-like functional is constructed to derive sampling-interval-dependent stability results. The Lyapunov-like functional has three features. First, it depends on time explicitly. Second, it may be discontinuous at the sampling instants. Third, it is not required to be positive definite between sampling instants. Moreover, the new Lyapunov-like functional can make use of the information fully of the sampled-data system, including that of both ends of the sampling interval. By making a new proposition for the Lyapunov-like functional, a sampling-interval-dependent stability criterion with reduced conservatism is derived. The new sampling-interval-dependent stability criterion is further extended to linear sampled-data systems with polytopic uncertainties. Finally, examples are given to illustrate the reduced conservatism of the stability criteria.     

Output-feedback control for sampled-data systems with variable sampling rate

In this paper, we propose design method of controller for sampled-data systems with variable sampling rate. First, we give design method for both H₂ and H_∞ controller. For H₂ control, performance of the system is introduced according to a standard sampled-data setting. A discrete-time H₂ control problem is employed for solving the original problem. Its solvability condition is then established as a parameter-dependent linear matrix inequality. A probabilistic approach is taken for coping with the parameter-dependency. H_∞ controller is designed by almost the same manner. Applying both results, we have design method for multi-objective control.     

Robust global uniform asymptotic stabilization of underactuated surface vessels with unknown model parameters

The full‐state stabilization scheme is proposed for the control of an underactuated surface vessel with unknown modeling parameters. By knowing only the upper/lower bounds of model parameters, the designed controller is the first one able to globally uniformly asymptotically stabilize all the states of the vessel to zero. The virtual surge velocity control law is first derived, which makes the Lyapunov function at the kinematic level non‐increasing, irrelevant to the yaw velocity, leaving a freedom for choosing the virtual yaw velocity control law to stabilize the other state variables. After finishing the design of virtual velocity law, the back‐stepping approach and the Lyapunov redesign technique are combined to obtain the actual force/torque control law despite parameter uncertainties. Simulation examples are given to illustrate the effectiveness of the proposed control law, showing that all the states and the control inputs are globally uniformly asymptotically convergent to zero under parameter uncertainties and are globally bounded under unknown external bounded disturbances. Copyright © 2013 John Wiley & Sons, Ltd.     

Global practical tracking of a class of nonlinear systems using linear sampled-data control

This paper considers the problem of global practical tracking via sampled-data control for a class of uncertain nonlinear systems. Under a lower triangular linear growth condition, a sampled-data state feedback controller is first constructed such that the states are globally bounded and the error between the system output and the reference signal will be rendered smaller than a given tolerance. When only the output of the system is measurable, a sampled-data output feedback controller, whose observer and control law are both linear, is constructed to solve the global practical tracking problem.     

Further results on sampled-data design for robust control of a single qubit

This paper presents further results on the robust control method for qubit systems in Dong et al. (2013) Dong, D., Petersen, I.R., &; Rabitz, H. (2013). Sampled-data design for robust control of a single qubit. IEEE Transactions on Automatic Control, 58, 2654–2659.[Crossref], [Web of Science ®] , [Google Scholar]. Based on the properties of an antisymmetric system, an alternative method is presented to analyse and exclude singularity intervals in the proof of partial original results. For the case of amplitude damping decoherence, a larger sampling period is presented when the upper bound of the probability of failure is small enough. For the case of phase damping decoherence, a larger sampling period is given when the lower bound of the target coherence is large enough. Furthermore, we provide improved sampling periods for amplitude damping decoherence and phase damping decoherence without the above prior constraints.     

Decentralised sampled-data control for large-scale systems with nonlinear interconnections

This paper presents a decentralised sampled-data control technique for a class of large-scale systems, which are considered to consist of linear subsystems and nonlinear interconnections. The decentralised sampled-data controller design problem is established using a closed-loop subsystem. Based on the controller design problem, the stability condition is derived for a closed-loop large-scale system, and the maximum interconnection bound is guaranteed to satisfy the stability condition. Also, its sufficient condition is formulated in terms of linear matrix inequalities. Finally, the effectiveness of the proposed technique is verified by using an example of the multi-machine power system.     

一类结构不确定采样系统的鲁棒控制

针对一类结构不确定性线性采样系统,在时域中用Lyapunov方法研究采样系统的鲁棒控制及最优鲁棒控制,给出了系统鲁棒稳定的充分条件以及相应的鲁棒控制律,控制律的求取借助于求解一类线性矩阵不等式（LMI）,或求解满足特定线性不等式条件下的优化问题,算例结果表明,采样周期是一个关键性的设计参数。     

A simple robust control for global asymptotic position stabilization of underactuated surface vessels

Global asymptotic stabilization of underactuated surface vessels is generally achieved only by designing complicated controllers. This paper proposes a very simple control law that globally asymptotically stabilizes the position of underactuated surface vessel to a desired constant location and its velocities to zero. The proposed controller is independent of velocity signals and is robust to model parameters. It neither includes an observer nor an adaptive/sliding‐mode law. Controller development and stability analysis rely on a novel Lyapunov function and LaSalle's theorem. Furthermore, by extending the proposed control strategy, a saturated control law is also obtained ensuring the semiglobal asymptotic stability of position error system. Effectiveness of the proposed control schemes is demonstrated by simulation examples. Copyright © 2017 John Wiley & Sons, Ltd.     

Stability and robust stability of positive linear Volterra difference equations

We first introduce a class of positive linear Volterra difference equations. Then, we offer explicit criteria for uniform asymptotic stability of positive equations. Furthermore, we get a new Perron–Frobenius theorem for positive linear Volterra difference equations. Finally, we study robust stability of positive equations under structured perturbations and affine perturbations. Two explicit stability bounds with respect to these perturbations are given. Copyright © 2008 John Wiley & Sons, Ltd.     

非线性采样控制系统的Lagrange稳定性

针对由具有外部慢时变输入信号的非线性被控对象和线性数字控制器构成的非线性采样系统,采用非线性跳跃系统方法及其线性化策略,得到了这类系统在理想离散化方式和无限字长数字控制器作用下(即不考虑量化因素)的Lagrange稳定(最终有界)条件.并指出,当考虑数字控制器和接口器件的非线性量化因素影响时,只要非线性量化环节及其相应偏导数有界,则所得稳定性结论仍然成立.