Sampled-data Systems Research Articles

Finite-time synchronization of sampled-data T–S fuzzy complex dynamical networks subject to average dwell-time approach

The problem of finite-time synchronization for Takagi–Sugeno (T–S) fuzzy complex dynamical networks with coupling delays via sampled-data control is presented in this paper. To change the sampled-data control system into a continuous time-delayed system, an input delay approach is applied. Based on the Lyapunov stability theory, a suitable Lyapunov–Krasovskii functional (LKF) is constructed with the Kronecker products. Furthermore, by applying the average dwell-time approach, a novel sufficient condition is established to ascertain the finite-time stabilization of fuzzy complex dynamical networks (CDNs) with switching signals. The proposed method is less conservative than conventional approaches, since the newly developed time-dependent fuzzy LKF is used. The proposed sufficient condition can be represented in the form of linear matrix inequalities (LMIs). Finally, the effectiveness and superiority of the proposed approach is validated through both numerical and practical examples.

Improved stability criteria for sampled-data systems using modified free weighting matrix

This paper investigates the stability analysis of sampled-data systems in the looped-functional framework. A modified free-weighting matrix inequality with quadratic-type is proposed to reduce conservatism of the integral term. Based on new looped-functional, improved conditions are derived in terms of linear matrix inequalities (LMIs) by utilizing the proposed integral inequality. Numerical examples show the superiority of the proposed condition through comparisons with the most recent results.

Explicit Computation of Sampling Period in Periodic Event-Triggered Multiagent Control Under Limited Data Rate

This paper investigates the coordination of nonlinear sampled-data multiagent systems subject to a data rate constraint. The purpose is to design resource-efficient communication and control strategies that guarantee exponential synchronization. Two implementation scenarios are considered: the period time-triggered control and the period event-triggered control. One of the main difficulties of the problem is to obtain an explicit formula for the maximum-allowable sampling period (MASP). To this end, an approach on finding the MASP for period time-triggered control is proposed first. Then, an asynchronous period event-triggered control strategy is formulated, and a communication function and a control function are designed for each agent to determine, respectively, whether the sampled state and control input should be transmitted at each sampling instant. Finally, the constraint of the limited data rate is considered. An observer-based encoder–decoder and a finite-level quantizer are designed, respectively, for the sensor-controller communication and the controller-actuator communication such that a certain constraint on the data rate is satisfied. It is shown that exponential synchronization can still be achieved in the presence of the data-rate constraint. A simulation example is given to illustrate the effectiveness of the theoretical results.

Group Consensus for Heterogeneous Multi-Agent Systems With Sampled and Quantized Data Under Directed Communication Topology

For a sampled-data heterogeneous multi-agent system (HMAS), this paper studies the group consensus problem under a directed topology, where the model of the HMAS is described by double integrators and single integrators. We design two group consensus protocols under different communication conditions. A sufficient condition is reported to guarantee that an HMAS can achieve group consensus asymptotically. Meanwhile, the final group consensus values of different groups are given. Furthermore, due to the bandwidth constraint existing in communication, the quantized group consensus is investigated. We also obtain a sufficient quantized group consensus condition. It is found that an HMAS can reach group consensus asymptotically under our protocol and the consensus errors almost converge to zero when the quantized errors tend to zero. Finally, this paper gives some simulation examples to show the validity of the theoretical analysis.

Identification and Accommodation of Control Actuator Faults Using Multi-rate Sampled Measurements

Abstract This work presents a model-based approach for the detection, estimation and accommodation of control actuator faults in dynamic processes controlled using multi-rate sampled state measurements. Initially, a model-based state feedback controller that employs an inter-sample model predictor to compensate for the unavailability of continuous state measurements is designed. Characterizations of both the stability and performance properties of the multi-rate sampled-data closed-loop system are obtained and expressed in terms of the measurement sampling rates, the magnitudes of the faults, and the various predictor and controller design parameters. A parameter estimator that estimates the magnitudes of the faults by minimizing the error between the estimated and sampled states over a moving horizon is then introduced and used to determine the fault or health status of the control actuators at the sampling times. The identification of faults triggers a fault accommodation scheme that adjusts selected predictor and controller design parameters to simultaneously preserve closed-loop stability and optimize a pre-defined performance metric. The implementation of the developed approach is illustrated using a simulated model of a solid oxide fuel cell system subject to both stability and performance-degrading actuator faults. A discussion of some of the intricacies of the multi-rate sampling scheme and how they impact the practical implementation of the fault identification and accommodation schemes is presented.

Stability Analysis of Sampled-Data Control Systems With Constant Communication Delays

This paper deals with the problem of stability for aperiodically sampled-data control systems with constant communication delays. Less conservative results are derived by two main techniques. First, a new looped-functional-based Lyapunov function is proposed, which considers the information of intervals $x({t_{k}})$ to $x(t)$ , $x(t)$ to $x({t_{k + 1}})$ , $x(t_{k}-\tau)$ to $x(t-\tau)$ , and $x(t-\tau)$ to $x(t_{k+1}-\tau)$ . Second, in the derivative of the Lyapunov function, the integral term which has the information of sampling-period plus communication delay is divided into three parts. Then, by employing integral inequality techniques, some improved stability conditions are derived. The numerical examples demonstrate the validity of the proposed methods.

Sampled-Data Control for Fuzzy Markovian Jump Systems With Actuator Saturation

In this article, the problem of sampled-data control is considered for fuzzy Markovian jump systems (FMJSs) with actuator saturation. Firstly, the mode-dependent lyapunov functional is constructed, which consists of a two-sided closed-loop function. On the basis of this function, stochastically stable criteria are presented in the form of linear matrix inequalities (LMIs). Then, based on the stochastically stable criteria, mode-dependent sampled-data controllers are designed for FMJSs. As a corollary, stable criteria and controller design are also proposed for the general aperiodic sampled-data linear system with actuator saturation. The improved LMI-based optimization conditions are obtained to estimate the region of attraction. Finally, numerical examples are provided to show the significant improvement of the presented method.

Synchronization of Coupled Nonlinear Systems with Bidirectional Sampled-data Couplings

This paper considers the synchronization problem of nonlinear systems with sampled-data couplings. In particular, we focus on full synchronization of two strictly semi-passive systems interconnected with sampled-data couplings. First, we show that the solution of the coupled sampled-data systems is ultimately bounded from the property of strict semi-passive systems. Then, we show the existence of the synchronization manifold and derive a sufficient condition for full synchronization of the systems. Finally, we show numerical simulation results with the Hindmarsh-Rose neuron systems to illustrate the validity of these theoretical results.

On the Local Input–Output Stability of Event-Triggered Control Systems

This paper studies performance preserving event design in nonlinear event-based control systems based on a local L2-type performance criterion. Considering a finite gain local L2-stable disturbance driven continuous-time system, we propose a triggering mechanism so that the resulting sampled-data system preserves similar disturbance attenuation local L2-gain property. The results are applicable to nonlinear systems with exogenous disturbances bounded by some Lipschitz-continuous function of state. It is shown that an exponentially decaying function of time, combined with the proposed triggering condition, extends the inter-event periods. Compared to the existing works, this paper analytically estimates the increase in intersampling periods at least for an arbitrary period of time. We also propose a so-called discrete triggering condition to quantitatively find the improvement in inter-event times at least for an arbitrary number of triggering iterations. Illustrative examples support the analytically derived results.

Robust output-feedback control for uncertain linear sampled-data systems: A 2D impulsive system approach

This paper deals with the sampled-data control problem based on state estimation for uncertain linear sampled-data systems. It is possible to show that the sampled-data control problem based on state estimation may be related with the conditions for the exponential stability of impulsive systems. Thus, a vector Lyapunov function-based approach, derived by means of a 2D time domain equivalence, is used for obtaining stability conditions of an impulsive system, and then, a solution to the observer-based control design problem is derived and expressed in terms of linear matrix inequalities. Some examples illustrate the feasibility of the proposed approach.

Model-based strategies for sensor fault accommodation in uncertain dynamic processes with multi-rate sampled measurements

This work presents model-based strategies for the accommodation of sensor faults in dynamic processes with multi-rate sampled state measurements. The developed strategies account explicitly for both closed-loop stability and performance considerations. Initially, a model-based feedback control system, in which a model predictor compensates for the unavailability of state measurements between sampling times, is designed. The stability and performance characteristics of the multi-rate sampled-data closed-loop system are analyzed and explicitly characterized in terms of the state sampling rates, the fault parameters, and the various process, model and controller design parameters. The resulting characterizations provide insight into the robustness and margins of tolerable faults that can be accommodated, and are used to develop both stability-based and performance-based fault accommodation schemes that aim to maintain closed-loop stability and minimize the degradation of closed-loop performance in the presence of sensor faults. Two types of sensor faults are considered. These include faults that manifest themselves as improper sensor readings, as well as faults that cause drift in the sensor sampling rate. The first type of fault introduces errors in the model state updates at the sampling times, while the second type of fault alters the rate at which the sensors sample the process states. The developed methods are illustrated through a case study involving a cascade of two non-isothermal continuous-stirred tank reactors with plant-model mismatch and access to full state measurements that are sampled at different rates. The case study gives some insight into the effects of sensor faults on the stability and performance of the sampled-data state feedback control system, and how these effects can be mitigated through use of fault-tolerant control.

Stability and stabilizability of discrete-time dual switching systems with application to sampled-data systems

In this paper, stability and stabilizability of discrete-time dual switching linear systems is investigated. The switched systems under consideration have two switching variables. One of them is stochastic, described by an underlying Markov chain; the other one can be regarded either as a deterministic disturbance or as a control input, leading to stability or stabilizability problems, respectively. For the considered class of systems, sufficient conditions for mean square stability (with or without control gain synthesis) and mean square stabilizability are provided in terms of matrix inequalities. When the stochastic switching is driven by an independent identically distributed sequence, we establish simpler conditions without additional conservatism. Then, it is shown how the proposed framework can be used to study aperiodic sampled-data systems with stochastic computation times. The results are illustrated on examples borrowed from the literature.

Exponential Consensus of Multiagent Systems With Lipschitz Nonlinearities Using Sampled-Data Information

In this paper, exponential consensus of general linear multiagent systems with Lipschitz nonlinear dynamics using sampled-data information is investigated. Both leaderless and leader-following consensuses are considered. Using input-delay approach, the resulting sampled-data closed-loop systems are first reformulated as continuous systems with time-varying delay in the control input. Then, decoupled conditions in terms of linear matrix equality (LMI) on the Lipschitz constant, the decay rate, the communication graph parameters, and the control gain matrix to guarantee exponential consensus are derived using novel Lyapunov functionals. Based on the sufficient conditions, controller design methods are also provided in the form of decoupled LMIs. Finally, simulation examples including the consensus of Chua’s circuit systems are given to illustrate the effectiveness of the obtained results.

Global sampled-data output feedback stabilization for a class of uncertain nonlinear systems

This paper investigates the global asymptotical stabilization using sampled-data output feedback (i.e., not all state information is available at the output) for a class of nonlinear systems which have uncontrollable and unobservable linearizations around the origin. A homogeneous version of Gronwall–Bellman inequality is introduced as the essential tool to estimate trajectory of nonlinear sampled-data control systems between two successive sampling instants. With the help of this new tool as well as the homogeneous domination approach, a sampled-data observer-based controller is constructed to globally asymptotically stabilize the origin of the nonlinear system under a homogeneous growth condition.

Polynomial LPV approach to robust H ∞ control of nonlinear sampled-data systems

This paper addresses -gain analysis and robust control of nonlinear sampled-data systems described by a polynomial linear parameter varying (PLPV) model. First, conditions for -gain analysis of sampled-data PLPV systems are derived using a modified Krasovskii functional in which the distance between the real and measured parameters are considered as uncertainties. The resulting conditions are formulated in terms of parameterised linear matrix inequalities (PLMI). Second, a solution approach for satisfying PLMI conditions over the set of whole parameters and uncertainties is proposed using the sum-of-squares decomposition method. Third, conditions for robust sampled-data controller synthesis for nonlinear systems described by PLPV models are derived in terms of parameterised bilinear matrix inequalities (PBMI) with the maximum allowable sampling period as the parameter. To make the resulting bilinear matrix inequality (BMI) problems tractable, an iterative algorithm is developed and utilised to solve the problem. Finally, the effectiveness of the proposed approach is verified using several real-world examples.

Hybrid mechanisms for robust synchronization and coordination of multi-agent networked sampled-data systems

We present a novel approach for the design of robust feedback coordination and control mechanisms for networks of asynchronous nonlinear multi-agent systems (MAS). Each agent corresponds to a sampled-data system characterized by a continuous-time plant, a discrete-time controller with logic or integer states, and a sampler/zero-order hold with a local clock. The goal is to robustly stabilize an application-dependent compact set defined a priori for the MAS, taking into account the asynchronous nature of the triggering mechanisms of the agents, and the limited information in the network. To solve this problem, we propose an emulation-like approach, where the feedback mechanism for each agent is initially designed for a nominal ideal synchronous MAS with a single logic state. Unlike existing emulation results for networked sampled-data systems with a single triggering mechanism, the implementation of multiple triggering mechanisms in MAS requires additional decentralized coordination algorithms to guarantee that the implemented system robustly emulates the behavior of the nominal synchronous system. Therefore, we propose a decentralized synchronization and coordination mechanism that controls the triggering mechanisms of the agents, guaranteeing robust stabilization of the closed-loop MAS. Our results are established by using Lyapunov tools, the invariance principle, and robustness corollaries for set-valued hybrid dynamical systems.

Stability Analysis of Linear Systems under Time-Varying Samplings by a Non-Standard Discretization Method

This paper is concerned with the stability of linear systems under time-varying sampling. First, the closed-loop sampled-data system under study is represented by a discrete-time system using a non-standard discretization method. Second, by introducing a new sampled-date-based integral inequality, the sufficient condition on stability is formulated by using a simple Lyapunov function. The stability criterion has lower computational complexity, while having less conservatism compared with those obtained by a classical input delay approach. Third, when the system is subject to parameter uncertainties, a robust stability criterion is derived for uncertain systems under time-varying sampling. Finally, three examples are given to show the effectiveness of the proposed method.

On stability for sampled-data nonlinear ADRC-based control system with application to the ball-beam problem

This paper mainly concerns with the stability analysis of the sampled-data nonlinear active disturbance rejection control (ADRC)-based control system. Firstly, a class of single-input-single-output (SISO) continuous plant is discretized using zero-order-hold (ZOH), and several kinds of digital implementation methods for the nonlinear extended state observer (NLESO) are newly proposed. Then the sampled-data nonlinear ADRC (NLADRC) based closed-loop system is transformed into a discrete-time Lurie-like system, to which linear matrix inequality (LMI)-based sufficient conditions for absolute stability and robust absolute stability are obtained. The sufficient conditions provide convenient and effective methods for determining the stability and its relationship with the parameters of the controller, the plant and the sampling period. Using the ball-beam system as an example, the proposed results are verified in both simulations and experiments.

Hierarchical Cucker–Smale flocking under random interactions with time-varying failure probabilities

This paper studies the hierarchical Cucker–Smale flocking model of sampled-data second-order discrete-time multi-agent systems under random interactions with time-varying failure probabilities. More precisely, each agent, at each sampling time point, can fail to see any of its superiors in the hierarchy. The random failures are not independent with varying failure rate probabilities. For this model with random interactions, we prove that the flocking would occur almost surely, i.e., agents’ velocities will converge almost surely to the velocity of the overall leader of the flock which moves with a varying velocity, the relative positions between agents and the overall leader converge almost surely. Finally, several numerical simulations are provided to illustrate the obtained results.

Stability and Stabilization Criteria for Sampled-data Control System via Augmented Lyapunov-Krasovskii Functionals

This paper proposes improved stability and stabilization conditions for sampled-data systems. Some newly augmented Lyapunov-Krasovskii functionals are constructed to derive enhanced conditions. First, a stability criterion for the sampled-data systems is established in terms of linear matrix inequalities (LMIs). Second, a controller design method is introduced in terms of nonlinear matrix inequalities (NLMIs). In order to solve the NLMI problem, cone complementarity linearization algorithm is introduced. Finally, numerical examples are included to show that the results obtained from the proposed method provide less conservative results, which support the superiority of our criteria.