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This paper addresses the problem of observer-based output feedback controller designs for discrete-time T–S fuzzy systems based on a relaxed approach in which the fuzzy Lyapunov functions are used. Different from the existing two-step method, a single-step linear matrix inequality method is provided for the observer-based controller design. It is shown that the controller and observer parameters can be obtained by solving a set of strict linear matrix inequalities that are numerically feasible with commercially available software. The new design method not only overcomes the drawback induced by the two-step approach but also provides less conservative results over some existing results. Finally, the effectiveness of the proposed approach is demonstrated by an example. [ABSTRACT FROM PUBLISHER]

This paper investigates the finite-time H∞ control problem for discrete-time Markovian jump linear systems with time delay and norm-bounded exogneous disturbance. The stochastic finite-time boundness is achieved by employing an average dwell time approach, which has more design freedom by allowing the stochastic Lyapunov-like function (SLLF) to increase more slowly during the running time of each operation mode. Note that the SLLF increases at every jumping instant rather than at every sampling time instant. Sufficient conditions for the solvability of the controller, which are dependent or independent on the time delay, are given in terms of linear matrix inequalities. Numerical examples are given to verify the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This article proposes a methodology for designing a partially mode delay dependent ℋ∞ controller design for discrete-time systems with random communication delays. Communication delays between sensors and controller are modelled by a finite state Markov chain where the transition probability matrix is partially known. Stability criteria are obtained based on Lyapunov–Krasovskii functional and a novel methodology for designing a partially mode delay dependent state feedback controller has been proposed. The controller is obtained by solving linear matrix inequality optimisation problems using cone complimentarity linearisation algorithm. A numerical example is provided to illustrate the effectiveness of the proposed controller. [ABSTRACT FROM PUBLISHER]

In this paper, a feedback model predictive control method is presented to tackle control problems with constrained multivariables for uncertain discrete-time nonlinear Markovian jump systems. An uncertain Markovian jump fuzzy system (MJFS) is obtained by employing the Takagi-Sugeno (T-S) fuzzy model to represent a discrete-time nonlinear system with norm bounded uncertainties and Markovain jump parameters. To achieve more generality, the transition probabilities of the Markov chain are assumed to be partly unknown and partly accessible. The predictive formulation adopts an on-line optimization paradigm that utilizes the closed-loop state feedback controller and is solved using the standard semi-definite programming (SDP). To reduce the on-line computational burden, a mode independent control move is calculated at every sampling time based on a stochastic fuzzy Lyapunov function (FLF) and a parallel distributed compensation (PDC) scheme. The robust mean square stability, performance minimization and constraint satisfaction properties are guaranteed under the control move for all admissible uncertainties. A numerical example is given to show the efficiency of the developed approach. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [ABSTRACT FROM AUTHOR]

The article considers stability and robust H∞ controller design of discrete-time systems with random communication delays and state quantization. A finite state Markov process is used to model communication delays between sensors and controllers. Measurements are assumed to be quantized by a logarithmic quantizer, and the effect of quantization errors are incorporated into the controller design. Based on a Lyapunov-Krasovskii approach, novel methodologies for analysing stability and designing a time-delay mode-dependent quantized state feedback controller are proposed. The controller is obtained through solving bilinear matrix inequalities (BMIs) using the cone complementarity linearisation algorithm. [ABSTRACT FROM AUTHOR]

In this work, the observer-based finite-time H ∞ control problem is studied for a class of discrete-time Markovian jump singular systems with time-varying norm-bounded disturbance. The main purpose of this paper is to design an observer and a state feedback controller ensuring that the resulting closed-loop error system is singular finite-time bounded via observer-based state feedback and satisfies a prescribed H ∞ performance level in a finite-time interval. By using the descriptor system approach presented by Fridman and Shaked, sufficient criteria on singular H ∞ finite-time stabilization via observer-based state feedback are derived in terms of linear matrix inequalities. A simulation example is also given to demonstrate the validity of the developed results. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with stochastic finite-time boundedness analysis for a class of uncertain discrete-time neural networks with Markovian jump parameters and time-delays. The concepts of stochastic finite-time stability and stochastic finite-time boundedness are first given for neural networks. Then, applying the Lyapunov approach and the linear matrix inequality technique, sufficient criteria on stochastic finite-time boundedness are provided for the class of nominal or uncertain discrete-time neural networks with Markovian jump parameters and time-delays. It is shown that the derived conditions are characterized in terms of the solution to these linear matrix inequalities. Finally, numerical examples are included to illustrate the validity of the presented results. [Copyright &y& Elsevier]

Abstract: This work studies the asynchronous H ∞ filtering problem for a class of discrete-time switched time-delay systems. The word “asynchronous” means that the switching of the filters has a lag to the switching of system modes due to the network induced random occurrences, which includes both the sensor saturations and the missing measurements. First, new results on the regional stability and l 2 gain analysis for the underlying system are given by allowing the Lyapunov-like function (LLF) to increase with a random probability during the unmatched period of the switching mode and the filter. Then, a regional H ∞ filter with a modified mode dependent ellipsoid constraint is designed such that the filtering error dynamics is asymptotically stable in the mean square sense with a given disturbance attenuation level. Finally, a numerical example is given to verify the efficiency of the proposed method. [Copyright &y& Elsevier]

Abstract: Quantization effects are inevitable in networked control systems (NCSs). These quantization effects can be reduced by increasing the number of quantization levels. However, increasing the number of quantization levels may lead to network congestion, (i.e., the network needs to transfer more information). In this paper, we investigate the problem of designing a robust  output feedback controller for discrete-time networked systems with an adaptive quantization density or limited information. More precisely, the quantization density is designed to be a function of the network load condition which is modeled by a Markov process. A stability criterion is developed by using the Lyapunov–Krasovskii functional and sufficient conditions for the existence of a dynamic quantized output feedback controller are given in terms of Bilinear Matrix Inequalities (BMIs). An iterative algorithm is suggested to obtain quasi-convex Linear Matrix Inequalities (LMIs) from BMIs. An example is presented to illustrate the effectiveness of the proposed design. [Copyright &y& Elsevier]