Review Article Analysis, Filtering, and Control for Takagi-Sugeno Fuzzy Models in Networked Systems

and Applied Analysis Volume 2015, Article ID 856390, 8 pages http://dx.doi.org/10.1155/2015/856390 2 Abstract and Applied Analysis a fascinating focus of research attracting constant attention. It is not surprising that there has been a rich body of relevant literature published in the past two decades; see, for example, [10–19] for control problems and [20–26] for filtering issues. In recent years, because of the ever-increasing popularity of communication networks, the study of networked systems has gradually become an active research area due to the advantages of using networked media in many aspects such as low cost, simple installation, reduced weight, and power requirements, as well as high reliability [27, 28]. It is well known that the signals are often transmitted through networks which may undergo unavoidable network-induced phenomena including communication delays, packet dropouts (also called missing measurements), signal quantization, and randomly occurring uncertainties (ROUs); see [29–37] and the references therein. These network-induced phenomena would bring in particular systems complexities (e.g., abrupt structural and parametric changes) which could seriously degrade the system performance if not adequately handled in practical engineering applications. Consequently, due to the merits of approximating nonlinear systems, the T-S fuzzy models in networked environments have been introduced to describe the nonlinear networked control systems (NCSs), and the corresponding control and filtering problems for suchT-S fuzzy systemswith aforementioned network-induced phenomena have attracted considerable attention by many researchers during the past few years [38–41]. In this paper, we focus mainly on the control and filtering problems for T-S fuzzy systems with network-induced phenomena and aim to provide a survey on some recent advances in this area. Firstly, a variety of T-S fuzzy control and filtering issues with network-induced phenomena are discussed in great detail. Both theories and techniques for dealing with the controller or filter design are systematically reviewed. Subsequently, latest results on T-S fuzzy control/filtering problems for networked systems are surveyed and some challenging issues for future research are raised. Finally, some conclusions are drawn and several possible related research directions are pointed out. The rest of the paper is organized as follows. In Section 2, the control and filtering problems for the T-S fuzzy systems with network-induced phenomena are reviewed. Section 3 reviews the latest results on T-S fuzzy control, filtering, and fault detection problems for networked systems and some challenging issues are highlighted at the same time. The conclusions and future work are given in Section 4. 2. T-S Fuzzy Control and Filtering with Network-Induced Phenomena The signal transmission via networked systems has become prevalent and, accordingly, the network-induced issues have drawn considerable research interest. In this section, we will recall the theoretical developments of T-S fuzzy control and filtering problems from the following four aspects: communication delays, packet dropouts, signal quantization, and ROUs. 2.1. T-S Fuzzy Control and Filtering with Communication Delays. It has been well recognized that communication delays, which could be one of the causes for poor performance or even instability of the closed loop, exist universally in practical systems. In the past decades, significant research efforts have been devoted to the control and filtering problems for T-S fuzzy systems with different types of time-delays including constant time-delays, time-varying delays,multiple time-delays, infinitely distributed time-delays,Markov jumping time-delays, and interval time-delays. For instance, in [42], some new results on stability properties (asymptotical stability and input-to-state stability) have been investigated for T-S fuzzy Hopfield neural networks with constant timedelay. Furthermore, in [33], the delay-dependent stabilizability condition has been integratedwith the shifted-Chebyshevseries approach and the hybrid Taguchi-genetic algorithm. An effective control scheme has been proposed to handle the quadratic finite-horizon optimal parallel distributed compensation (PDC) control problem of the T-S fuzzymodel-based time-delay systems. In order to overcome the inherent difficulty of the nonlinear optimal control issue, the corresponding design has been turned into the feasibility problem for certain linear matrix inequalities (LMIs) in a suboptimal sense that can be easily solved by means of numerically efficient convex programming algorithms. In the context of T-S fuzzy control, in addition to the communication delays, other factors contributing to the system complexities have also been studied. For example, the parameter uncertainties are unavoidable for modeling real-world engineering systems which would result in perturbations of the elements of a system matrix [43–45]. As such, in the past decade, considerable attention has been devoted to fuzzy systems with various time-delays and parameter uncertainties, and a large number of results have been reported by exploiting the LMI approach. According to the linear differential inclusion state-space representation, a novel design scheme of fuzzy controller has been proposed in [46] to stabilize the nonlinear multiple time-delay largescale system. Moreover, the H ∞ performance index, which is closely related to the robustness of the closed-loop system, also has been employed to evaluate the design controller. In [47], the robustH ∞ control problemhas been investigated for a class of discrete-time T-S fuzzy systems with the infinitely distributed time-delay which can be regarded as the discretization version of the infinite integral form in continuoustime case. It deserves attention that, in most of the literature mentioned above, the control problem has been considered for the case that the time-delay is not random. However, the time-delays may occur in a probabilistic method. So, stochastic time-delays over T-S fuzzy control systems also have been further researched. For instance, a T-S model has been employed to represent a networked control system with Markov jumping time-delays in [48], and the designed approach has addressed situations involving all possible network-induced delays. In [49], the probabilistic interval distribution of communication delay has been taken into account, and a robust networked controller for a class of T-S fuzzy systems has been designed, where the solvability of the networked controller design depends not only on the upper Abstract and Applied Analysis 3and Applied Analysis 3 and lower bounds of the delay but also on its probability distribution. Similar to the control problem with communication delays, the problemofT-S fuzzy filtering also has been attracting considerable research interests and a lot of advanced methods have been proposed to handle the network-induced time-delays. For example, the fuzzy H ∞ filtering has been discussed in [50] for a class of nonlinear discrete-time systems with both multiple time-delays and unknown bounded disturbances. For the same kind of time-delays, in [51], a full-order H ∞ filter has been designed to guarantee that the filtering error dynamics are stochastically stable and the given H ∞ attenuation level is guaranteed. Additionally, it is worth mentioning that the results discussed above have been presented with delay-independent conditions. An interesting research problem is how to utilize the time-delay information to reduce the conservatism. Based on such an idea, the delay-dependent approach has been widely adopted in recent years for various time-varying delay T-S fuzzy systems. For instance, by utilizing the T-S fuzzy model, the H ∞ filtering problem has been addressed in [52] for a class of nonlinear systemswhere the nonlinearities have been assumed to satisfy global Lipschitz conditions. Furthermore, a novel delaydependent piecewise Lyapunov-Krasovskii functional, which is dependent on both the upper bound of the delays and the delay interval, has been constructed in [30] to analyze the filtering error dynamics and then some sufficient conditions have been established in terms of LMIs. Very recently, for the delay-dependent problems mentioned above, a novel technique has been provided by introducing some free-weighting matrices. The delay-dependent filter design for nonlinear systems with time-varying delay via T-S fuzzy model approach has been studied in [53], and the main technique used is the free-weighting matrix method combined with a matrix decoupling approach. The problem of delay-dependent robust H ∞ filtering design has been investigated for a class of uncertain discrete-time statedelayed T-S fuzzy systems in [54], where the state delay has been assumed to be time-varying and of an interval-like type, meaning that both the lower and upper bounds of the timevarying delay are available. Based on the delay-dependent piecewise Lyapunov-Krasovskii functional combined with an improved free-weighting matrix method, a delay-dependent H ∞ filter has been further designed for a class of discretetime nonlinear interconnected systems with time-varying delays via the T-S fuzzy model in [55], and it guarantees both the delay-dependent stability and the prescribed H ∞