There are many communication imperfections in networked control systems (NCS) such as varying transmission delays, varying sampling/transmission intervals, packet loss, communication constraints and quantization effects. Most of the available literature on NCS focuses on only some of these aspects, while ignoring the others. In this paper we present a general framework that incorporates communication constraints, varying transmission intervals and varying delays. Based on a newly developed NCS model including all these network phenomena, we will provide an explicit construction of a continuum of Lyapunov functions. Based on this continuum of Lyapunov functions we will derive bounds on the maximally allowable transmission interval (MATI) and the maximally allowable delay (MAD) that guarantee stability of the NCS in the presence of communication constraints. The developed theory includes recently improved results for delay-free NCS as a special case. After considering stability, we also study semi-global practical stability (under weaker conditions) and performance of the NCS in terms of Lp gains from disturbance inputs to controlled outputs. The developed results lead to tradeoff curves between MATI, MAD and performance gains that depend on the used protocol. These tradeoff curves provide quantitative information that supports the network designer when selecting appropriate networks and protocols guaranteeing stability and a desirable level of performance, while being robust to specified variations in delays and transmission intervals. The complete design procedure will be illustrated using a benchmark example.

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Networked Control Systems With Communication Constraints: Tradeoffs Between Transmission Intervals, Delays and Performance

This paper is concerned with the design of mode-dependent and mode-independent filters for continuous-time linear Markovian jump systems (MJSs) with time-varying delays. Different from the existing studies in the literature, the purpose of this paper is to solve the H∞, L2 - L∞ passive and dissipative filtering problems in a unified framework. This purpose is successfully realized by using a new performance index that is referred to as extended dissipativity. The extended dissipative inequality contains several weighting matrices. By tuning the weighting matrices, the extended dissipativity will reduce to the H∞ performance, L2 - L∞ performance, passivity and dissipativity, respectively. Delay-dependent conditions for the analysis of stochastic stability and extended dissipativity for MJSs with time-varying delays are obtained by using a mode-dependent Lyapunov-Krasovskii functional together with a novel integral inequality. Based on these conditions, the design methods for mode-dependent and mode-independent filters are developed based on linear matrix inequalities. The designed filters guarantee that the resulting filtering error system is stochastically stable and extended dissipative for any admissible delays. Finally, the effectiveness of the proposed methods is substantiated with three illustrative examples.

Filtering of Markovian Jump Delay Systems Based on a New Performance Index

This paper is concerned with the problems of stability and dissipativity analysis for static neural networks (NNs) with time delay. Some improved delay-dependent stability criteria are established for static NNs with time-varying or time-invariant delay using the delay partitioning technique. Based on these criteria, several delay-dependent sufficient conditions are given to guarantee the dissipativity of static NNs with time delay. All the given results in this paper are not only dependent upon the time delay but also upon the number of delay partitions. Some examples are given to illustrate the effectiveness and reduced conservatism of the proposed results.

Stability and Dissipativity Analysis of Static Neural Networks With Time Delay

Robust control of uncertain systems: Classical results and recent developments

This paper is concerned with decentralized event-triggered dissipative control for systems with the entries of the system outputs having different physical properties. Depending on these different physical properties, the entries of the system outputs are grouped into multiple nodes. A number of sensors are used to sample the signals from different nodes. A decentralized event-triggering scheme is introduced to select those necessary sampled-data packets to be transmitted so that communication resources can be saved significantly while preserving the prescribed closed-loop performance. First, in order to organize the decentralized data packets transmitted from the sensor nodes, a data packet processor (DPP) is used to generate a new signal to be held by the zero-order-hold once the signal stored by the DPP is updated at some time instant. Second, under the mechanism of the DPP, the resulting closed-loop system is modeled as a linear system with an interval time-varying delay. A sufficient condition is derived such that the closed-loop system is asymptotically stable and strictly $ {(Q_{0},S_{0},R_{0})}$ -dissipative, where $ {Q_{0},S_{0}}$ , and $ {R_{0}}$ are real matrices of appropriate dimensions with $ {Q_{0}}$ and $ {R_{0}}$ symmetric. Third, suitable output-based controllers can be designed based on solutions to a set of a linear matrix inequality. Finally, two examples are given to demonstrate the effectiveness of the proposed method.

A Decentralized Event-Triggered Dissipative Control Scheme for Systems With Multiple Sensors to Sample the System Outputs

This book presents a fully revised and expanded treatment of dissipative systems theory. It examines linear and nonlinear systems with examples of both in each chapter; some infinite-dimensional examples are also included. Throughout emphasis is placed on the use of the dissipative properties of a system for the design of stable feedback control laws. This second edition is substantially reorganized both to accommodate new material and to enhance its pedagogical properties. The main value of the book is that it us an up-to-date reference of dissipative systems in the framework of many system descriptions. It is a good roadmap to the many contributions on the subject. It is a good reference for dissipative systems for advanced engineering students and researchers in control, however quantity was obtained at the cost of pedagogical quality; an opportunity was missed to create an interesting textbook for these categories. The text is recommended for its vast amount of timely information and indications to the literature. However, the latter information could have been better filtered and structured to provide a unified basic deep knowledge of the field of dissipative systems, which can be mentally reconstructed by the student reader.

F. M. Callier

Papers

Dissipative Systems Analysis and Control: Theory and Applications (2nd Edition)-[Book review; B. Brogliato, R. Lozano, B. Maschke]