Stochastic Stability of Networked Control Systems with Network-induced Delay and Data Dropout

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

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.

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.

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.

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.

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.

Improved stability and stabilization design for networked control systems using new quadruple-integral functionals

Based on the controlled process that is linear time-invariant system, the network-induced long time delay is viewed as time-varying parameter uncertainties. The uncertainty parameters model of networked control systems with long time delay is set up. The existing conditions of asymptotic stability for networked control system with long time delay are presented by Lyapunov method and robust control theory. The design method of stabilization controller for networked control system is proposed in terms of linear matrix inequalities. In the end the simulation based on the networked control unstable system is studied. The simulation results show the proposed controller is feasible and effective.

Network-induced delays and packet dropouts are relevant issues that can degrade networked control systems' performance and may even lead to instability. This paper concerns the establishment of a stability criterion for networked control systems (NCSs) consisting of an LTI process and a dynamic feedback controller. Conditions for stability are provided in terms of Linear Matrix Inequalities (LMIs), whose solution yields network-induced delay upper bounds. Numerical examples and a simulation ratify the theoretical results.

Exponential stability of networked control systems with network-induced random delaysIn this paper, the problem of exponential stability for the standard form of the state control, realized in a networked control system structure, is studied. To deal with the problem of stability analysis of the event-time-driven modes in the networked control systems the delayed-dependent exponential stability conditions are reformulated and proven. Based on the delay-time dependent Lyapunov-Krasovskii functional, exponential stability criteria are derived. These criteria are expressed as a set of linear matrix inequalities and their structure can be modified to use the bilinear inequality techniques.

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

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.

International audience