Stability Analysis of T–S Fuzzy Control System With Sampled-Dropouts Based on Time-Varying Lyapunov Function Method

Stability analysis for a class of switched systems with state constraints via time-varying Lyapunov functions

This paper focuses on the fault-tolerant control (FTC) of networked control systems (NCSs) with packet dropouts using switched system approach. The basic idea is to model such NCSs as a discrete-time switched system. Thus, the FTC of such NCSs can be reduced to that of switched systems. Sufficient conditions are presented about the stabilization of NCSs. Stabilizing switched state/output feedback controllers can be constructed by solving a set of linear matrix inequalities (LMIs), which can be easily tested with efficient LMI algorithms. The maximum allowable dropout bound can be obtained by solving an optimization problem.

The aim of this article is to address the modeling and control problems of discrete-time Takagi–Sugeno (T-S) fuzzy systems that are affected by stochastic packet dropouts. To describe the stochastic behavior of packet dropout between the sensor–controller and controller–actuator, a consecutive packet dropout model is employed. By treating consecutive packet dropouts (CPDs) as an extension of the transmission interval, the considered T-S system is transformed into a stochastic system with bounded stochastic input delay. In addition, a novel equivalent model for the closed-loop system is proposed, which captures the nonuniform distribution of the input delay caused by CPDs. Using the obtained equivalent model, it is possible to evaluate the probability distribution of each stochastic input delay value using the formula for total probability. This approach allows us to fully consider the probability information of CPDs in subsequent stability analysis and controller design. Based on this model, delay-probability dependent stability conditions are derived using stochastic Lyapunov functionals, and controller design conditions are also provided. Finally, the correctness and conservatism reduction of the proposed design method are demonstrated using numerical examples of two physical systems described by T-S fuzzy models.

The problem of stabilization for wireless networked control system (NCS) with packet dropout and time delay is studied in this article. The impulsive control law for the NCS is defined with time delay and impulse. Using a switching model, the network‐induced imperfections can be treated as three switching subsystems. Therein, in the case of packet dropout, the control law use the previous state via the first‐order hold. The impulsive control law is designed using the switched system approach and the average dwell time method. The obtained sufficient conditions which can guarantee the exponential stability of switched system are in the form of linear matrix inequalities. Finally, a numerical example is used to demonstrate the merits and applicabilities of the proposed method. © 2015 Wiley Periodicals, Inc. Complexity 21: 291–299, 2016

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

Although the conventional fuzzy PID controller can track and adjust the output of network adaptively, the effect of compensation is not obvious for time delay and packet dropout. To reduce the influence caused by time delay and packet dropout in networked control system (NCS), an improved Smith fuzzy PID controller based on TrueTime toolbox is proposed in this paper, the result of simulation showed this new model is more effective not only in obtaining better output performance in time delay and packet dropout, but also more stable and reliable in different protocols over conventional fuzzy PID controller.

SUMMARYThe discrete‐time and continuous‐time fuzzy systems with quantization and packet dropout are considered in this paper. The quantizer used here is a uniform one with arbitrary quantization regions, and the packet dropout process is modeled as a time‐homogenous Markov process. Because of the properties of packet dropout process, the fuzzy systems considered here are seen as Markov jump fuzzy systems, and the theories of Markov jump system are used to discuss the mean square stability of the closed‐loop systems. On the basis of the zoom strategy and Lyapunov theory, for the given failure rate and recovery rate, sufficient conditions are given for the closed‐loop fuzzy systems to be mean square stable, and the feedback controllers are designed to ensure the stability of fuzzy systems. A single link direct joint driven manipulator model is presented to show the effectiveness of the main results. Copyright © 2013 John Wiley & Sons, Ltd.

In this chapter, we consider the \(H_\infty \) filtering of wireless networked systems with a time-varying transmission protocol and random packet dropout. First, a switched system approach is employed to model the time-varying transmission process of each sensor. Then, the packet dropout phenomenon is modeled by a set of Bernoulli stochastic variables.

This paper studies the problem of adaptive eventtriggered dynamic output feedback fuzzy control for nonlinear networked control systems. Two crucial factors, packet dropouts and actuator failure, are taken into consideration simultaneously. Takagi-Sugeno fuzzy model is introduced to describe considered systems. The Bernoulli random distribution process is employed to depict the phenomenon of data missing. The actuator failure model is adopted to depict actuator failure. An innovative adaptive event-triggered strategy is built to save computational resource. In the light of Lyapunov stability theory, a fuzzy dynamic output feedback controller is designed to guarantee the stochastic stability and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance for considered systems. Finally, simulation results are provided to demonstrate the usefulness of the proposed control strategy.

The importance of distributed aircraft engine control architecture is well discussed in literature. The performance of distributed engine control systems is predominantly dependent on the performance of the communication network. Communication constraints such as time delays and packet dropouts can lead to inconsistent data latency, which may limit the performance of distributed engine control or in the worst case scenario, can even destabilize the control system. In this paper, we review three different partially distributed engine control architectures based on ARINC 825, a general standardization of Controller Area Network (CAN) for aerospace applications. The first architecture employs the legacy sensors & legacy actuators and uses a data concentrator to transmit the data to distributed FADEC. Second architecture, which has smart sensors and legacy actuators, makes use of state observers to provide compensation for sensor-controller time delays. In the third architecture, smart actuators allows the use of network predictive controller, which provides compensation for time delays and packet dropouts in both sensor-controller and controlleractuator communication channels. Stability conditions for each of the three architectures are presented and the three architectures are compared on the basis of performance and robustness to time delays and packet dropouts.

This paper is concerned with quantitative analysis and synthesis for continuous-time networked control systems (NCSs) with packet dropouts and interval time-varying sampling period. A new packet dropout separation method is proposed to separate packet dropouts from the sum of network-induced delay and packet dropouts, and an interval time-varying sampling period approach is presented to model the variation of sampling period. Then, a novel packet dropout decomposition based Lyapunov functional is constructed, and the quantitative relationships between packet dropout probability and stability and stabilization of NCSs are established. A numerical example is given to illustrate the merits and effectiveness of the proposed methods.

This paper studies the networked control systems (NCSs) with bilateral time-varying delay and packet dropout, and proposes a novel active time-varying sampling period switched control method to make the system stable. Firstly, the event and time-driven sensor is adopted, and its variable sampling period is designed to follow the change of time delay and packet dropout simultaneously. Then the discrete-time switched systems with uncertain parameters are modeled by using the method of augmented matrix, and the condition satisfying exponential stability of the system state is obtained based on the approach of average dwell time. The obtained condition further establishes the quantitative relation between the exponential decay rate and the packet dropout rate. This method overcomes the problem of long delay and packet disordering in NCSs. Finally the simulation result illustrates the effectiveness of the proposed method.

Investigating the positive effects of packet dropouts on network-based [formula omitted] control for a class of linear systems

This paper is concerned with the asymptotic stability issue for a class of stochastic Takagi–Sugeno (TS) fuzzy systems with time-varying delays. Then, by utilizing a delay-fractioning method, the stochastic analysis theory combined with the matrix inequality technique, a new set of sufficient condition in terms of linear matrix inequalities is presented which ensures the asymptotic stability of the stochastic TS fuzzy systems with time-delays. The results obtained in this paper are delay-dependent in the sense that they depend on not only the lower bound but also the upper bound of the time-varying delay. Numerical examples are given to illustrate the effectiveness and less conservativeness of the obtained results.

The insertion of communication networks in closed-loop of digital control systems makes the system synthesis and analysis complex. In this paper, we consider the combination of classical reliability, risk and safety evaluation with typical control system through digital networked control systems. The main purpose is to study the influence of transmission delays and packet dropouts on the reliability of digital networked control systems by using a modified statistical method-Monte Carlo simulation. The behaviors of two types of fault are modelled by different statistical distribution. The control strategies we apply for digital control systems are Proportion Integration Differentiation control strategies, generated by Genetic Algorithm. In terms of a realistic system model, we evaluate and compare the influences on the reliability of digital networked control systems with different control strategies from quantitative aspect. Numerical examples are presented to illustrate the effectiveness and correctness of the approach.