Stability criteria of uncertain networked control systems

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

The paper presents stabilization of a Networked Control System (NCS) with uncertain, time-varying delays using two stabilization approaches namely, Parameter Dependant Lyapunov Function (PDLF) and Quadratic Lyapunov Function (QLF). The PDLF approach depends upon the time varying delay parameters. Thus, for larger delays the system's stability is ensured. In NCS, the uncertainties arising out from the variations in time-delay is modeled using polytopic approach and the stability region of the system is presented in terms of controller gain and maximum tolerable delay. The overall NCS is represented in discrete domain. The proposed PDLF stabilization results have been compared with that of the QLF approach. Lyapunov-based stability criterion is presented in Linear Matrix inequalities (LMIs). The stabilized state feedback controller is designed using LMIs and considering the bounded time-varying delays. The proposed approach is illustrated by two numerical examples. From the results obtained, it is observed that the PDLF approach improves the stability region of the system.

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.

Driven by recent telecommunication demand, shared communication channels are more abundant today than ever before. These shared wired/wireless networks for communication are being exploited more and more in control systems to connect sensors, controllers and actuators resulting in so-called networked control systems (NCSs). NCSs replace the more traditional control systems where dedicated point-to-point (wired) connections are being used. The advantages of using NCS technology are inexpensive and easily modifiable communication links which allow control algorithms to be easily implemented in situations where dedicated connections are not possible (either economically or physically). However, the drawback is that the control system is susceptible to undesirable (possibly destabilizing) side-effects such as time-varying transmission intervals, time-varying delays, packet dropouts, quantization and a shared communication medium. These network-induced effects undermine fundamental assumptions on which traditional control theory is built and, therefore, it is essential to develop new techniques and tools that can be used to analyze and/or design control systems which communicate via a shared network. This thesis advances NCS analysis and design methodologies by contributing new theoretical developments, new software tools and new experimental validation results. The first new theoretical development is in the area of analyzing robust stability properties with respect to network-induced effects. A sum of squares (SOS) approach for a class of nonlinear NCSs incorporating bounded time-varying delays, bounded time-varying transmission intervals and a shared communication medium is developed. Mathematical models that describe these nonlinear NCSs are cast into suitable hybrid system formulations. Based on these hybrid system formulations, (families of) Lyapunov functions are constructed using SOS techniques. Amongst other benefits, it is shown that this technique improves the guaranteed robustness margins compared to existing work. The second new theoretical development concerns the design of networkaware decentralized controllers guaranteeing robust stability properties with respect to network-induced effects. We develop one of the first approaches based on semidefinite programming techniques to synthesize stabilizing decentralized observer-based output-feedback controllers for linear plants where the controllers, sensors and actuators are connected via a shared communication network subject to time-varying transmission intervals and delays. To effectively deal with the shared communication medium, a switched observer structure is adopted that switches based on the transmitted measured outputs and a switched controller structure is also adopted that switches based on the transmitted control inputs at each transmission time. By taking a discrete-time switched linear system perspective on modeling these decentralized NCSs, we are able to derive a general model that captures all these networked and decentralized control aspects. We provide linear matrix inequality (LMI)-based synthesis conditions which, if satisfied, provide stabilizing observer-based controllers that are both decentralized and robust to network effects. Regarding new software tools, the first prototype of a toolbox is developed to automate (robust) stability analysis (and controller design) for NCSs. Specifically, it is shown that the toolbox can be employed to efficiently verify if a linear time-invariant (LTI) plant and an LTI controller interconnected with a shared network are robust to certain network imperfections. The main intention of the toolbox is to make the available theory readily accessible to and applicable for the general control community. Additionally, the chosen software structure enables the incorporation of custom models or custom stability/performance analysis conditions in an easy manner, thereby allowing the control community to contribute and to further develop the toolbox. Finally, an experimental case study involving a wirelessly controlled inverted pendulum/cart system is investigated. In particular, the communication network itself is analyzed such that the network-induced effects can be characterized in terms of bounds on the transmission intervals and transmission delays. Based on these bounds, the prototype toolbox is applied to analyze the robustness regions for different performance specifications, which aid in tuning the controller to achieve more closed-loop robustness with respect to the network-induced effects. This leads to a validation of the developed theory in an experimental setting. In addition to the validation of the developed theory, many new insights into the network behavior are obtained and explained, thereby raising new interesting questions for future research on NCSs.

This article addresses the problem of controller design for networked control systems over digital communication. The systems under consideration are stabilised via state feedback, where the effects of sampled signal, state quantisation, network-induced delay and packet dropout are considered. The proposed delay-dependent stability criteria are formulated in the form of a linear matrix inequality, which ensure asymptotic stability and a prescribed H ∞ performance level for networked control systems with admissible uncertainties. Maximum allowable delay bound of networked control systems is obtained by solving a convex optimisation problem. Furthermore, a numerical example is given to illustrate the effectiveness of the main result.

Networked control of AC microgrid

This paper is concerned with the stability of networked control systems in the discrete-time domain. A new bounding technique is proposed to estimate some finite-sum terms appearing in the forward difference of the chosen Lyapunov functional. This new bounding technique can provide tighter upper bounds for some finite-sum terms and avoid overly bounding for the finite-sum terms. Then a novel delay-dependent stability criterion is derived by using this new bounding technique. Compared with some existing stability criteria in the published literature, the novel stability criterion is proven theoretically to be less conservative and is shown to be of smaller numerical complexity.

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.

In this article, we characterize the joint effects of plant uncertainty, transmission delay, and fading channel on the stabilization problem of networked control systems (NCSs). We assume that the controller remotely controls the plant and the control packet is transmitted over a delayed and fading channel. We formulate the integrated system as an uncertain discrete-time stochastic system with both input delay and multiplicative noise. The innovative contributions of this article are described as follows. We propose a set of necessary and sufficient conditions for stabilizing an uncertain-free system. Moreover, for the general uncertain model, we derive the necessary and sufficient stabilization condition in terms of symmetric matrix homogeneous polynomials, which can be verified by linear matrix inequality (LMI) feasibility test. As an application, under the parallel transmission strategy, we derive an explicit formula for computing the maximum allowable delay bound, which is uniquely determined by system parameters and signal-to-noise ratio.

Delay-dependent robust stability criteria of uncertain stochastic systems with time-varying delay

The use of avionics networks for flight control system has reduced aircraft weight, system installation, integration and maintenance costs as well as introduced time delays and structured uncertainties. This paper studies the robust stability and stabilisation problem of uncertain networked flight control system with random time delays. Some new sufficient criteria with simple mathematical forms for robust stability and stabilisation of networked flight control system are derived by a free weighting matrix approach. A memoryless state feedback robust controller and the maximum bound of time delay are obtained based on the solution of linear matrix inequalities (LMIs) which are established by the Lyapunov-Krasovskii stability theory. Numerical examples are given to illustrate the effectiveness of design procedure.

Time-delay is unavoidable, encountered in many practical systems such as networked control systems, communication networks, manufacturing, and biology. On the one hand, it often represents a source of instability and oscillation. On the other hand, the appearance of delay can have a stabilizing effect, and delayed feedback control can be used to stabilize some unstable systems. Considering its theoretical and practical importance, increasing attention has been focused on the analysis and synthesis of time-delay systems, and various new approaches have been proposed to reduce their conservatism. The aim of reducing the conservatism of delay-dependent stability criteria is to establish new stability criteria to provide a maximal allowable delay as large as possible. Among different techniques, the reduced conservatism is mainly obtained by constructing an improved Lyapunov functional and employing a tighter bound on some weighted cross products. A great number of effective methods have been provided such as delay-partitioning method, convex combination method, Wirtinger-based inequality, and Bessel–Legendre inequality.

In this paper, we present an improved delay-dependent absolute stability criterion for Lur’e systems with time delays. The guarantee of absolute stability is provided by Lyapunov-Krasovskii theorem with the Lyapunov functional containing the integral of sector-bounded nonlinearities. The Lyapunov functional terms involving delay are partitioned to be associated with each equidistant fragment on the length of time delay. Employing the Jensen inequality and S-procedure, the sufficient condition is derived from time derivative of the Lyapunov functional. Then, the absolute stability criterion expressed in terms of linear matrix inequalities (LMIs) can be efficiently solved using available LMI solvers. The bisection method is used to determine the maximum allowable time delays to ensure the stability of Lur’e systems in the presence of uncertain time-invariant delays. In addition, the stability criterion is extended to Lur’e systems subject to norm-bounded uncertainties by using the matrix eliminating lemma. Numerical results from two benchmark problems show that the proposed criteria give significant improvement on the maximum allowable time delays.

This paper deals with time delays which exist in networked control systems due to presence of communication network. Time delay impact on networked control system stability is analyzed, and some relations for maximum allowable delay bound estimation are given as well. It is shown, on example of DC motor control, that the system behaves in desired manner and remains stable when appropriate values of regulator parameters are chosen to match estimated maximum time delay.

This paper investigates the robust stability for a class of uncertain neutral system with time-varying delay and nonlinear uncertainties. A new delay-dependent stability criteria is presented by using Lyapunov method. The stability criteria for such systems in terms of linear matrix inequalities (LMIS). Some numerical examples show that the effectiveness and the significantly important over some existing results.