Robust global stabilisability by means of sampled-data control with positive sampling rate

This work proposes a notion of robust reachability of one set from another set under constant control. This notion is used to construct a control strategy, involving sequential set-to-set reachability, which guarantees robust global stabilisation of non-linear sampled data systems with positive sampling rate. Sufficient conditions for robust reachability of one set from another under constant control are also provided. The proposed method is illustrated through a number of examples, including the study of the sampled-data stabilisation problem of the chemostat.     

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.     

Periodic sampling: maximising the sampling period

The process of periodic sampling is investigated for a class of nonlinear systems. The objective is to achieve the longest sampling period that is compatible with a specified error bound. It is shown that there are robust optimal controllers that achieve this objective. It is also shown that the performance of such optimal controllers can be approximated by bang-bang controllers – controllers that are relatively easy to design and implement.     

Stabilisation analysis for switched neutral systems based on sampled-data control

In this paper, the problem of stabilisation analysis for switched neutral systems based on sampled-data control and average dwell time approach is investigated. Delay-dependent stabilisation results are derived in terms of linear matrix inequalities by constructing piecewise Lyapunov–Krasovskii functional based on the Wirtinger's inequality. Also, the controller gain matrix is designed by applying an input-delay approach. Further convex combination technique and some integral inequalities are used to derive less conservative results. The effectiveness of the derived results is validated through numerical examples.     

Computer control under time-varying sampling period: An LMI gridding approach

This paper addresses computer control under time-varying sampling period and delayed actuation. The proposed approach uses time-varying observers and state-feedback controllers designed by means of linear matrix inequalities (LMI) and quadratic Lyapunov functions. The use of non-stationary Kalman filters is also discussed. A separation principle applies in some cases. A DC motor control setup shows the applicability of the approach in a real implementation.     

间接型的混杂模型参考自适应控制

针对相对阶为1的理想系统,本文考虑了具有混杂自适应律的间接型模型参考自适应控制问题.通过建立系统和控制器的离散参数估计和它们的插值四者之间关系的性质,严格地分析了闭环系统的稳定性,证明了闭环系统中所有的信号都一致有界,并且跟踪误差渐进收敛于零.     

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.     

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.     

Cooperative output synchronisation of networked feedforward nonlinear systems via linear sampled-data control

This paper studies the problem of cooperative output synchronisation of networked feedforward nonlinear systems via linear sampled-data control. To dominate the unknown nonlinear perturbing terms, a scaling gain is introduced by a change in coordinates. Then, we construct a reduced-order sampled-data observer and use the backstepping method to design a linear sampled-data controller. By using combined graph theory with feedback domination approach, an explicit formula for the sampling period can be obtained under the proposed controller with appropriate gains such that all outputs of the agents in the network can be synchronised. Finally, two examples are provided to verify the effectiveness of the proposed method.     

Allowable sampling period for consensus control of multiple general linear dynamical agents in random networks

This article studies the consensus problem for a group of sampled-data general linear dynamical agents over random communication networks. Dynamic output feedback protocols are applied to solve the consensus problem. When the sampling period is sufficiently small, it is shown that as long as the mean topology has globally reachable nodes, the mean square consensus can be achieved by selecting protocol parameters so that n???1 specified subsystems are simultaneously stabilised. However, when the sampling period is comparatively large, it is revealed that differing from low-order integrator multi-agent systems the consensus problem may be unsolvable. By using the hybrid dynamical system theory, an allowable upper bound of sampling period is further proposed. Two approaches to designing protocols are also provided. Simulations are given to illustrate the validity of the proposed approaches.     

Finite-time quantised feedback asynchronously switched control of sampled-data switched linear systems

This paper studies the problem of stabilising a sampled-data switched linear system by quantised feedback asynchronously switched controllers. The idea of a quantised feedback asynchronously switched control strategy originates in earlier work reflecting actual system characteristic of switching and quantising, respectively. A quantised scheme is designed depending on switching time using dynamic quantiser. When sampling time, system switching time and controller switching time are all not uniform, the proposed switching controllers guarantee the system to be finite-time stable by a piecewise Lyapunov function and the average dwell-time method. Simulation examples are provided to show the effectiveness of the developed results.     

Random stabilization of sampled-data control systems with nonuniform sampling

For a sampled-data control system with nonuniform sampling, the sampling interval sequence, which is continuously distributed in a given interval, is described as a multiple independent and identically distributed (i.i.d.) process. With this process, the closed-loop system is transformed into an asynchronous dynamical impulsive model with input delays. Sufficient conditions for the closed-loop mean-square exponential stability are presented in terms of linear matrix inequalities (LMIs), in which the relation between the nonuniform sampling and the mean-square exponential stability of the closed-loop system is explicitly established. Based on the stability conditions, the controller design method is given, which is further formulated as a convex optimization problem with LMI constraints. Numerical examples and experiment results are given to show the effectiveness and the advantages of the theoretical results.     

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.     

Passivity-based non-fragile control for Markovian jump delayed systems via stochastic sampling

This paper studies the problem of non-fragile passive control for Markovian jump delayed systems via stochastic sampling. The Markovian jumping parameters, appearing in the connection weight matrices and in two additive time-varying delay components, are considered to be different. The controller is assumed to have either additive or multiplicative norm-bounded uncertainties. The sampled-data with stochastic sampling is used to design the controller by a discontinuous Lyapunov functional. This functional fully utilises the sawtooth structure characteristics of the sampling input delay. By using the matrix decomposition method and some newly inequalities, sufficient conditions are obtained to guarantee that for all admissible uncertainties the system is robustly stochastically passive. Illustrative examples are provided to show the effectiveness of the results.     

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.     

交换式以太网控制系统传感器变采样调度研究

针对基于交换式以太网的网络化控制系统的数据传输和控制性能优化问题,提出了传感器根据给定值与实测值差额的绝对值对照静态调度表变采样周期的调度优化方法.使用TrueTime 2.0工具箱搭建了交换式以太网控制系统仿真平台进行仿真研究,并与定采样周期方法进行了对比,仿真结果验证了其可行性.此方法在实际的工程应用中具有一定的参考价值.     

Design of output feedback consensus controllers for nonlinear sampled-data multi-agent systems of strict-feedback form

Design of reduced-order observer-based output feedback consensus controllers for nonlinear sampled-data multi-agent systems of strict-feedback form is considered based on nonlinear sampled-data control and consensus control theories. As a practical application of the proposed design method, output feedback consensus control for sampled-data fully actuated ships is also discussed.     

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.     

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.