Generalized sampled data feedback control of distributed parameter systems

In the sampled-data control literature there are necessary conditions and sufficient conditions for stabilizability of distributed parameter systems by generalized sampled-data control. For finite-dimensional systems the necessary conditions are also known to be sufficient. We show that this equivalence extends to the infinite-dimensional case if the underlying semigroup is analytic. However, for general systems, the necessary conditions are not sufficient, nor are the sufficient conditions necessary. We prove this by a single example with a free parameter – one choice of parameter shows that the necessary conditions are too weak, and another choice shows that the sufficient conditions are too strong.     

Null controllability with vanishing energy for discrete-time systems

In this paper null controllability with vanishing energy for discrete-time systems is considered. As in the case of continuous time systems necessary and sufficient conditions in terms of an algebraic Riccati equation are given. Then necessary and sufficient conditions involving the eigenvalues of the state matrix are given. Reachability and controllability with vanishing energy are also considered and necessary and sufficient conditions for them are given. Finally applications to sampled-data systems, systems with impulse control and periodic systems are discussed.     

Ripple-free deadbeat control for sampled-data systems

In this paper the ripple-free deadbeat control problem for sampled-data systems is considered. This control objective is to settle the error to zero for all time after some finite settling time, in other words to eliminate the ripples between the sampling instants in deadbeat control of sampled-data systems. The necessary and sufficient conditions to solve this problem are derived and related to the system type, and a method of constructing the ripple-free deadbeat control system is presented.     

Robustness With Respect to Sampling for Stabilization of Riesz Spectral Systems

We suppose that a continuous-time feedback is input–output stabilizing for an infinite-dimensional system. We address the question of whether the sampled-data controller obtained by applying idealized sample-and-hold to this continuous-time feedback is also input–output stabilizing if the sampling time is small enough. This question has been previously addressed for fairly general systems under various conditions. In this note, we restrict our attention to Riesz spectral systems, for which we generalize the existing results. Specifically, we give two relatively simple conditions which, combined, are sufficient for the sampled-data controller to be stabilizing. The first condition is a spectrum decomposition for the open-loop system generator, which by itself is necessary, but not sufficient, for the system to be stabilizable by sampled-data control. The second is a summability condition relating the real part of the spectrum of the generator and the expansion coefficients for the input and feedback operators.     

非线性采样系统指数稳定的新条件

研究了非线性采样系统的稳定性问题. 对以采样周期为参数的离散时间系统族, 证明了全局指数稳定的Lyapunov定理和逆定理. 分别基于系统的一般近似模型和Euler近似模型, 给出了闭环系统全局指数稳定的新条件. 与现有结果相比, 取消了Lyapunov函数全局Lipschitz连续的假设, 减弱了闭环系统全局指数稳定的充分条件.     

On observability of sampled-data systems

In this paper we consider sampled-data systems derived from continuous, time-invariant systems whose inputs are piecewise constant. The problem dealt with is that of finding necessary and sufficient conditions for observability of the sampled-data system, given that the continuous-time system is observable. By comparison With some previously obtained results pertaining to the preservation of controllability under sampling, it is shown that the latter requires a stronger condition than that required for the preservation of observability.     

On the necessity of looped-functionals arising in the analysis of pseudo-periodic,sampled-data and hybrid systems

Looped-functionals have been shown to be relevant for the analysis of a wide variety of systems. However, the conditions obtained in previous papers on the analysis of sampled-data, impulsive and switched systems have only been shown to be sufficient for the characterisation of their associated discrete-time stability conditions. We prove here that these conditions are also necessary. This result is derived for a wider class of linear systems, referred to as impulsive pseudo-periodic systems, that encompass periodic, impulsive, sampled-data and switched systems as special cases.     

Stability analysis of sampled-data systems via open-/closed-loop characteristic polynomials contraposition

In this paper, a class of sampled-data systems with double feedbacks are scrutinized for internal/external stability through the open-/closed-loop characteristic polynomials contraposition. A sampled-data system with double feedbacks consists of a continuous-time plant and two feedback control loops: a discrete-time one for digital control objectives with sampler and zero-order hold synchronized, and a continuous-time one for analog control performances. Contraposition stability criteria are worked out by exploiting what we call the contraposition return difference relationship in between the open- and closed-loop characteristic polynomials defined via the lifted model. The criteria for asymptotical stability are necessary and sufficient, independent of open-loop poles distribution of the lifted model and locus orientation specification. Moreover, the criteria for L_p-stability are sufficient, while retaining the technical merits of the criteria for asymptotical stability. All criteria present stability conditions in the standard discrete-time sense that are implementable either graphically with loci plotting, or numerically without loci plotting. Examples are included to illustrate the results.     

On robust stability of linear systems

In this paper the robust stability of linear continuous and discrete systems in the frequency domain is considered giving necessary and sufficient conditions. Based on that, the method of Tsypkin and Polyak (1991) is proved in a simple way. Extensions to discrete systems in the z-domain and sampled-data systems in the delta-domain are done using two ways of parametrization.     

Sampled-data output feedback control of a class of uncertain nonlinear systems

In this paper, we study the problem of sampled-data output feedback control for a class of uncertain nonlinear systems. The main contributions of this work are two-fold: (i) we develop a systematic design procedure of sampled-data output feedback controller; and (ii) we provide a theoretical analysis of the sampled-data closed-loop system, which shows that the state of the plant can be regulated into any given neighborhood of the origin by an appropriate choice of design parameters and sampling period. Furthermore, the bound of the neighborhood is proportionally dependent on the sampling period. Finally, an illustrative example is given to demonstrate the effectiveness of the presented method.     

Achievable H performance in sampled-data smoothing: beyond the -barrier

The lifting technique is a powerful tool for handling the periodically time-varying nature of sampled-data systems. Yet all known solutions of sampled-data H^∞ problems are limited to the case when the feedthrough part of the lifted system, , satisfies , where γ is the required H^∞ performance level. While this condition is always necessary in feedback control, it might be restrictive in signal processing applications, where some amount of delay or latency between measurement and estimation can be tolerated. In this paper, the sampled-data H^∞ fixed-lag smoothing problem with a smoothing lag of one sampling period is studied. The problem corresponds to the a-posteriori filtering problem in the lifted domain and is probably the simplest problem for which a smaller than performance level is achievable. The necessary and sufficient solvability conditions derived in the paper are compatible with those for the sampled-data filtering problem. This result extends the scope of applicability of the lifting technique and paves the way to the application of sampled-data methods in digital signal processing.     

二阶多智能体系统采样控制的一致性

研究在固定拓扑和切换拓扑下,二阶多智能体系统通过采样控制的一致性问题。首先,对于固定拓扑,给出了二阶多智能体系统通过采样控制达到一致性的充要条件;其次,对于切换拓扑,在所有联合切换拓扑有生成树的前提下,建立基于控制参数和采样周期使二阶系统实现一致性的充分条件。最后,用数值仿真验证所给结论的有效性。     

Adaptive sampled-data based linear quadratic optimal control of stochastic systems

The problem of sampled-data (SD) based adaptive linear quadratic (LQ) optimal control is considered for linear stochastic continuous-time systems with unknown parameters and disturbances. To overcome the difficulties caused by the unknown parameters and incompleteness of the state information, and to probe into the influence of sample size on system performance, a cost-biased parameter estimator and an adaptive control design method are presented. Under the assumption that the unknown parameter belongs to a known finite set, some sufficient conditions ensuring the convergence of the parameter estimate are obtained. It is shown that when the sample step size is small, the SD-based adaptive control is LQ optimal for the corresponding discretized system, and sub-optimal compared with that of the case where the parameter is known and the information is complete.     

自适应事件触发控制的多智能体系统一致性

研究了拓扑结构为有向强连通图的多智能体系统的一致性问题。提出一种新的自适应事件触发控制方案,根据采样数据动态调整触发时间间隔,提高了系统的控制性能。基于Lyapunov稳定性理论和线性矩阵不等式方法,得到多智能系统渐进趋于一致的充分条件。同时,得到一致性条件与触发参数和通信拓扑有关的结论,数值仿真结果进一步验证了理论分析的有效性。     

Robust performance of periodic systems

Robust performance of sampled-data systems to structured periodic and quasi-periodic uncertainty is considered, and necessary and sufficient conditions are derived, The conditions are finite dimensional, and explicitly computing them is investigated; the results are illustrated with an example. This work is readily extended to yield exact and finite dimensional robust performance conditions for structured arbitrary time-varying uncertainty     

Sampled-data H ∞ control for networked control systems with digital control inputs

In this article, the problem of sampled-data H _∞ control for networked control systems (NCSs) with digital control inputs is considered, where the physical plant is modelled as a continuous-time one, and the control inputs are discrete-time signals. By exploiting a novel Lyapunov–Krasovskii functional, using the Leibniz–Newton formula and a free-weighting matrix method, sufficient conditions for sampled-data H _∞ performance analysis and H _∞ controller design for such systems are given. Since the obtained conditions of H _∞ controller design are not expressed strictly in term of linear matrix inequalities, the sampled-data H _∞ controller is solved using modified cone complementary linearisation algorithm. In addition, the new sampled-data stability criteria for the NCSs is proved to be less conservative than some existing results. Numerical examples demonstrate the effectiveness of the proposed methods.     

From Continuous-Time Design to Sampled-Data Design of Observers

In this work, a sampled-data nonlinear observer is designed using a continuous-time design coupled with an inter-sample output predictor. The proposed sampled-data observer is a hybrid system. It is shown that under certain conditions, the robustness properties of the continuous-time design are inherited by the sampled-data design, as long as the sampling period is not too large. The approach is applied to linear systems and to triangular globally Lipschitz systems.     

Continuous-time controller redesign for digital implementation: A trajectory based approach

Given a continuous-time nonlinear closed loop system, we investigate sampled-data feedback laws for which the trajectories of the sampled-data closed loop system converge to the continuous-time trajectories with a prescribed rate of convergence as the length of the sampling interval tends to zero. We derive necessary and sufficient conditions for the existence of such sampled-data feedback laws and—in case of existence—provide explicit redesign formulas and algorithms for these controllers.     

H2 and H∞ control forinfinite-dimensional systems with jumps

We consider a semigroup model with jumps in the state that covers distributed parameter systems with impulse control or sampled-data distributed parameter systems with control realized through zero-order or first-order hold. We then introduce the H₂ and H_∞ problems for this system and give the solutions in terms of the solutions of Riccati equations with jumps