Engang Tian

A Delay System Method for Designing Event-Triggered Controllers of Networked Control Systems

This note is concerned with event-triggered H∞ controller design for networked control systems. A novel event-triggering scheme is proposed, which has some advantages over some existing schemes. A delay system model for the analysis is firstly constructed by investigating the effect of the network transmission delay. Then, based on this model, criteria for stability with an H∞ norm bound and criteria for co-designing both the feedback gain and the trigger parameters are derived. These criteria are formulated in terms of linear matrix inequalities. Simulation results have shown that the proposed event-triggering scheme is superior to some existing event-triggering schemes in the literature.

Delay-dependent stability analysis and synthesis of uncertain T--S fuzzy systems with time-varying delay

This paper considers the delay-dependent stability analysis and controller design for uncertain T-S fuzzy system with time-varying delay. A new method is provided by introducing some free-weighting matrices and employing the lower bound of time-varying delay. Based on the Lyapunov-Krasovskii functional method, sufficient condition for the asymptotical stability of the system is obtained. By constructing the Lyapunov-Krasovskii functional appropriately, we can avoid the supplementary requirement that the time-derivative of time-varying delay must be smaller than one. The fuzzy state feedback gain is derived through the numerical solution of a set of linear matrix inequalities (LMIs). The upper bound of time-delay can be obtained by using convex optimization such that the system can be stabilized for all time-delays. The efficiency of our method is demonstrated by two numerical examples.

Delay-Distribution-Dependent Stability and Stabilization of T–S Fuzzy Systems With Probabilistic Interval Delay

In this paper, we are concerned with the problem of stability analysis and stabilization control design for Takagi-Sugeno (T-S) fuzzy systems with probabilistic interval delay. By employing the information of probability distribution of the time delay, the original system is transformed into a T-S fuzzy model with stochastic parameter matrices. Based on the new type of T-S fuzzy model, the delay-distribution-dependent criteria for the mean-square exponential stability of the considered systems are derived by using the Lyapunov-Krasovskii functional method, parallel distributed compensation approach, and the convexity of some matrix equations. The solvability of the derived criteria depends not only on the size of the delay but also on the probability distribution of the delay taking values in some intervals. The revisions of the main criteria in this paper can also be used to deal with the case when only the information of variation range of the delay is considered. It is shown by practical examples that our method can lead to very less conservative results than those by other existing methods.

Stabilization of Systems With Probabilistic Interval Input Delays and Its Applications to Networked Control Systems

Motivated by the study of a class of networked control systems, this correspondence paper is concerned with the design problem of stabilization controllers for linear systems with stochastic input delays. Different from the common assumptions on time delays, it is assumed here that the probability distribution of the delay taking values in some intervals is known a priori. By making full use of the information concerning the probability distribution of the delays, criteria for the stochastic stability and stabilization controller design are derived. Traditionally, in the case that the variation range of the time delay is available, the maximum allowable bound of time delays can be calculated to ensure the stability of the time-delay system. It is shown, via numerical examples, that such a maximum allowable bound could be made larger in the case that the probability distribution of the time delay is known.

Quantized output feedback control for networked control systems

This paper addresses the problem of output feedback control for networked control systems (NCSs) with limited communication capacity. Firstly, we propose a new model to describe the non-ideal network conditions and the input/output state quantization of the NCSs in a unified framework. Secondly, based on our newly proposed model and an improved separation lemma, the observer-based controller is developed for the asymptotical stabilization of the NCSs, which are shown in terms of nonlinear matrices inequalities. The nonlinear problems can be computed through solving a convex optimization problems, and the observed and controller gains could be derived by solving a set of linear matrix inequalities. Thirdly, two simulation examples are given to demonstrate the effectiveness of the proposed method.

New stability criteria of neural networks with interval time-varying delay: A piecewise delay method

Abstract This paper provides improved conditions for the global asymptotic stability of a class of neural networks with interval time-varying delays. A piecewise delay method is firstly proposed. In this method, the variation interval of the time delay is divided into two subintervals by introducing its central point. Then, by constructing a new Lyapunov–Krasovskii functional and checking its variation in the two subintervals, respectively, some new delay-dependent stability criteria for the addressed neural networks are derived. Numerical examples are provided to show that the achieved conditions are less conservative than some existing ones in the literature.

A delay distribution based stability analysis and synthesis approach for networked control systems

Communication delays in networked control systems (NCSs) has been shown to have non-uniform distribution and multifractal nature. This paper proposes a delay distribution based stability analysis and synthesis approach for NCSs with non-uniform distribution characteristics of network communication delays. A stochastic control model related with the characteristics of communication networks is established to describe the NCSs. Then, delay distribution-dependent NCS stability criteria are derived in the form of linear matrix inequalities (LMIs). Also, the maximum allowable upper delay bound and controller feedback gain can be obtained simultaneously from the developed approach by solving a constrained convex optimization problem. Numerical examples showed that the results derived from the proposed method are less conservativeness than those derived from the existing methods.

Improved delay-dependent robust stabilization conditions of uncertain T--S fuzzy systems with time-varying delay

This paper aims to develop simplified yet improved delay-dependent robust control for uncertain T-S fuzzy systems with time-varying delay. This is achieved through constructing new Lyapunov-Krasovskii functionals and improving Jensens inequality. Unlike existing work in this area, the approach developed in this paper employs neither free-weighing matrices nor model transformations. As a result, simplified yet improved stability conditions are obtained for T-S fuzzy systems with norm-bounded-type uncertainties. For controller synthesis of the fuzzy systems, the stabilization problem with memoryless state feedback control is solved via utilizing a cone complementarity minimization algorithm. Numerical examples are given to demonstrate the effectiveness of the proposed approach.

Robust delay-distribution-dependent stability of discrete-time stochastic neural networks with time-varying delay

A robust delay-distribution-dependent stochastic stability analysis is conducted for a class of discrete-time stochastic delayed neural networks (DSNNs) with parameter uncertainties. The effects of both variation range and distribution probability of the time delay are taken into account in the proposed approach. The distribution probability of time delay is translated into parameter matrices of the transferred DSNNs model, in which the parameter uncertainties are norm-bounded, the stochastic disturbances are described in term of a Brownian motion, and the time-varying delay is characterized by introducing a Bernoulli stochastic variable. Some delay-distribution-dependent criteria for the DSNNs to be robustly globally exponentially stable in the mean square sense are achieved by Lyapunov method and introducing some new analysis techniques. Two numerical examples are provided to show the effectiveness and applicability of the proposed method.

T–S Fuzzy Model-Based Robust Stabilization for Networked Control Systems With Probabilistic Sensor and Actuator Failure

The system studied in this paper has four main features: 1) It is a networked controlled system (NCS), and therefore, the signal transfer is subject to random delay and/or loss; 2) it is a nonlinear system approximated by a Takegi--Sugeno (T-S) fuzzy model; 3) its multisensors and multiactuators are subject to various possible faults/failures; and 4) there are uncertainties in the plant model parameters. A comprehensive model is first developed in this paper to cover these features for a class of NCS nonlinear systems. This model has removed some limitations of similar models in the published literature. Then, the Lyapunov functional and the linear matrix inequality (LMI) are applied to develop two new stability conditions (Theorems 1 and 2). These conditions and an algorithm are used to design a controller to achieve robust mean square stability of the system. Finally, two examples are used to demonstrate the application of the modeling and the controller design method developed.