Exponential stability of networked control systems with network-induced random delays

The problem of stabilization of networked control systems (NCSs) with time-varying transmission delays is investigated. The time-varying delays lie in any two adjoining sampling instants of the plant. A technique is proposed for designing stabilizing controllers by converting NCSs with time-varying transmission delays into parameter uncertain systems with constant input delay, then the theory of robust stabilization of delay systems can be applied to solving this problem. Sufficient condition on stabilization of such NCSs is developed in terms of linear matrix inequality.

Recent technological advances have enabled distributed control systems to be implemented via networks. This allows feedback control loops to be closed over a shared communication channel. Network-induced delays are inevitable, however, when transmitting digital data between control devices. This paper analyzes the stability of such networked control systems (NCS). We first review some previous work on this topic, offering some improvements. We analyze the influence of the sampling rate and network delay on system stability. We further study the stability of NCS using a hybrid system stability analysis technique.

Output feedback stabilization for Markov-based nonuniformly sampled-data networked control systems

The presence of a communication network in a control loop induces many imperfections such as varying transmission delays, varying sampling/transmission intervals, packet loss, communication constraints and quantization effects, which can degrade the control performance significantly and even lead to instability. Various techniques have been proposed in the literature for stability analysis and controller design for these so-called networked control systems. The aim of this chapter is to survey the main research lines in a comprehensive manner.

New stability criteria and stabilization methods on networked control systems (NCSs) with short time-varying delay (STVD) are proposed in this paper. An NCS with STVD is transformed into a time-varying discrete time system. And then, this discrete time system is converted into a equivalent time-invariant system with norm-bounded uncertainties by using robust control techniques. Using this method, the conservatism of the stability condition caused by STVD can be reduced. Based on that, a single norm-bounded uncertainty is replaced by N norm-bounded uncertainties to further reduce conservatism. Theoretical analysis shows that when N is increased, the stability condition becomes less conservative. For a fixed sampling period, the obtained stability conditions explicitly depend on the upper and lower bounds of the time delay. The existence condition and design method for the controllers are also presented. Finally, three numerical examples are provided to demonstrate the effectiveness of the proposed scheme.

In this paper, we derive a necessary and sufficient condition for stability of networked control systems (NCSs) in the mean square sense and introduce the packet dropping margin to determine the robustness of the system with respect to packet dropping. By analyzing the relationship between the packet dropping probability and stability robustness, it is shown that a controller designed by a robust pole assignment approach makes the system less sensitive to packet dropping.

This paper concerns the problem of the model, stability and controller design for networked control system (NCS) with time-varying delay and dropped out packet. For the NCS with time-varying delay and data packet dropout, four new control methods of dynamical state feedback control, dynamical state feedback proportional-integral (PI) control, state feedback proportional-derivative (PD) control and dynamical state feedback PD control are presented. The NCS with time-varying delay and data packet dropout based on the four control methods is modeled as an asynchronous dynamical system (ADS) constrained by event rates. Furthermore, based on the ADS theory, principle of Lyapunov stability and method of linear matrix inequality, both the semi-negative definite matrix conditions of exponential stability and the controller design for NCS are given. Finally, numerical example illustrates the feasibility of the results.

The problem of stabilization of networked control systems (NCSs) with data packet dropout is studied. Sufficient conditions are presented on the stability and stabilization of the NCSs with packet dropout. The novelty of this work lies in that NCSs with arbitrary but finite data packet dropout are modelled as switched linear systems, and this enables us to apply the result of switched systems to the analysis and synthesis of such NCSs. The admissible upper bound of the dropped packets can be determined by a set of linear matrix inequalities (LMIs) which guarantee the stability of the NCSs. Stabilizing controllers (via state feedback and static output feedback) can be constructed by solving a set of LMIs. Also, for an NCS with a convergence rate constraint, similar results are obtained. Examples are worked out to illustrate the effectiveness of the proposed method

The stochastic stabilisation of networked control systems is investigated with a special focus on the lossy multi‐packet transmission in the wireless communication context. The resulting partially available system states due to multi‐packet transmission are firstly reconstructed at the controller, and the sufficient conditions for stochastic stability are then given for the closed‐loop system, which finally leads to a controller design method with explicit consideration of multi‐packet transmission. The proposed theoretical results are verified by both numerical and TrueTime‐based examples.

Delay-dependent stability criteria for a class of networked control systems with multi-input and multi-output☆

Research on mean square exponential stability of networked control systems with multi-step delay

A wireless networked control systems (NCS) is a control system whose feedback path is realized over a wireless communication network. The stability of such systems can be problematic given the random way in which wireless channels drop feedback messages. This paper establishes sufficient conditions for the almost sure stability of NCS under random dropouts. These conditions relate the burstiness in the dropout process to the nominal response of the controlled system. In particular, this means that the burstiness of the dropout process provides a convenient quality-of-service (QoS) constraint on the wireless channel that can be used to adaptively reconfigure the control system in a manner that guarantees the almost sure stability of the NCS. We also show how a probabilistic extension of the network calculus can be used to reconfigure multi-hop communication networks so this paper's sufficient stability condition is not violated.

This paper studies the problem of the exponential stability of networked control systems (NCSs) with large delay periods, which often appear in the transmission of NCSs. Some new concepts about large delay periods are introduced, and a method based on switching is employed. The maximum allowable transfer interval is obtained such that the considered system is exponentially stable. The criteria obtained contain existing results without considering a large delay period as a special case. An example is given to show the effectiveness of the proposed criteria. Copyright © 2009 John Wiley & Sons, Ltd.

A new control mode is proposed for a networked control system whose network-induced delay is longer than a sampling period. A time-division algorithm is presented to implement the control and for the mathematical modeling of such networked control system. The infinite horizon controller is designed, which renders the networked control system mean square exponentially stable. Simulation results show the validity of the proposed theory.

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