Observer-Based Relaxed ${{cal H}}_{infty }$ Control for Fuzzy Systems Using a Multiple Lyapunov Function

This short paper proposes a method of designing a fuzzy observer-based H _infin controller for discrete-time Takagi-Sugeno (T-S) fuzzy systems. To enhance the applicability of the output-feedback controller and improve its performance, this short paper first builds a set of fuzzy control rules with premise variables different from those of the T-S fuzzy system, and sets the overall controller to be dependent on not only the current time but also the one-step-past information on the estimated fuzzy weighting functions. Then, based on the fuzzy control rules, this short paper establishes a less conservative H _infin stabilization condition incorporated with a multiple Lyapunov function dependent on the estimated fuzzy weighting functions. Through a two-step design procedure, the H _infin stabilization condition is formulated in terms of parameterized linear matrix equalities (PLMIs), which are reconverted into LMIs with the help of an efficient and effective relaxation scheme.     

Relaxed ${cal H}_{infty }$ Stabilization Conditions for Discrete-Time Fuzzy Systems With Interval Time-Varying Delays

To derive less-conservative delay- and range-dependent ${cal H}_{infty }$ stabilization conditions for discrete-time Takagi–Sugeno (T–S) fuzzy systems with interval time-varying delays, the use of a fuzzy-weighting-dependent Lyapunov–Krasovskii functional (FWLKF), in which all variables are set to be affinely or quadratically dependent on fuzzy weighting functions, is proposed. Subsequently, parameterized linear matrix inequality (PLMI)-based ${cal H}_infty$ stabilization conditions are derived by following the free-weighting matrix approach. To fully exploit the convexity of fuzzy weighting functions, the derived PLMIs are sequentially replaced by a finite set of LMIs by considering all possible conditions associated with fuzzy weighting functions.      

${cal H}_{infty}$ Filtering of Discrete-Time Markov Jump Linear Systems Through Linear Matrix Inequalities

This technical note addresses the discrete-time Markov jump linear systems ${cal H}_{infty}$ filtering design problem. First, under the assumption that the Markov parameter is measurable, the main contribution is the linear matrix inequality (LMI) characterization of all linear filters such that the estimation error remains bounded by a given ${cal H}_{infty}$ norm level, yielding the complete solution of the mode-dependent filtering design problem. Based on this result, a robust filter design able to deal with polytopic uncertainty is considered. Second, from the same LMI characterization, a design procedure for mode-independent filtering is proposed. Some examples are solved for illustration and comparisons.      

Simultaneous $H^{infty}$ Control for Nonlinear Systems

This note develops a novel method for designing simultaneous $H^{infty}$ state feedback controllers for a collection of single-input nonlinear systems. Based on the Kalman—Yakubovich—Popov Lemma, necessary and sufficient conditions for the existence of simultaneous $H^{infty}$ controllers are derived by the control storage function approach. A universal formula for constructing continuous, time-invariant, simultaneous $H^{infty}$ state feedback controllers is presented.      

$ {cal L}_{2}$ Gain of Periodic Linear Switched Systems: Fast Switching Behavior

We investigate the $ {cal L}_{2}$ gain of periodic linear switched systems under fast switching. For systems that possess a suitable notion of a time-average system, we characterize the relationship between the ${cal L}_{2}$ gain of the switched system and the ${cal L}_{2}$ gain of its induced time-average system when the switching rate is sufficiently fast. We show that the switched system ${cal L}_{2}$ gain is in general different from the average system ${cal L}_{2}$ gain if the input or output coefficient matrix switches. If only the state coefficient matrix switches, the input-output energy gain for a fixed ${cal L}_{2}$ input signal is bounded by the ${cal L}_{2}$ gain of the average system as the switching rate grows large. Additionally, for a fixed ${cal L}_{2}$ input, the maximum pointwise in time difference between the switched and average system outputs approaches zero as the switching rate grows.      

Decentralized $H_{infty }$ Filter Design for Discrete-Time Interconnected Fuzzy Systems

This paper describes a decentralized $H_{infty }$ filter design for discrete-time interconnected fuzzy systems based on piecewise-quadratic Lyapunov functions. The systems consist of $J$discrete-time interconnected Takagi–Sugeno (T–S) fuzzy subsystems, and a decentralized $H_infty$ filter is designed for each subsystem. It is shown that the stability of the overall filtering-error system with $H_{infty }$ performance can be established if a piecewise-quadratic Lyapunov function can be constructed. Moreover, the parameters of filters can be obtained by solving a set of linear matrix inequalities that are numerically feasible. Two simulation examples are given to show the effectiveness of the proposed approach.      

Delay-Dependent $hbox{H}_{infty }$ Filter Design for Discrete-Time Fuzzy Systems With Time-Varying Delays

This paper investigates delay-dependent $hbox{H}_{bminfty }$ filter design problems for discrete-time fuzzy systems with time-varying delays. First, a novel delay-dependent piecewise Lyapunov–Krasovskii functional (DDPLKF) is proposed in which both the upper bound of delays and the delay interval are considered. Based on this DDPLKF, the delay-dependent stability criteria for discrete-time systems with constant or time-varying delays are obtained, respectively. Then, delay-dependent full-order and reduced-order $hbox{H}_{bminfty }$ filter design approaches are proposed. The filter parameters can be obtained by solving a set of linear matrix inequalities (LMIs). Simulation examples are also given to illustrate the performance of the proposed approaches. It is shown that our approaches are less conservative and that the corresponding $hbox{H}_{bminfty }$ filters can achieve better performance than the existing approaches.      

$H_{bm infty}$ Fuzzy Filtering of Nonlinear Systems With Intermittent Measurements

This paper is concerned with the problem of H _infin fuzzy filtering of nonlinear systems with intermittent measurements. The nonlinear plant is represented by a Takagi-Sugeno (T-S) fuzzy model. The measurements transmission from the plant to the filter is assumed to be imperfect, and a stochastic variable satisfying the Bernoulli random binary distribution is utilized to model the phenomenon of the missing measurements. Attention is focused on the design of an H _infin filter such that the filter error system is stochastically stable and preserves a guaranteed H _infin performance. A basis-dependent Lyapunov function approach is developed to design the H _infin filter. By introducing some slack matrix variables, the coupling between the Lyapunov matrix and the system matrices is eliminated, which greatly facilitates the filter-design procedure. The developed theoretical results are in the form of linear matrix inequalities (LMIs). Finally, an illustrative example is provided to show the effectiveness of the proposed approach.     

$H_{infty }$ Fuzzy Control of Nonlinear Systems Under Unreliable Communication Links

This paper investigates the problem of H _infin fuzzy control of nonlinear systems under unreliable communication links. The nonlinear plant is represented by a Takagi--Sugeno (T-S) fuzzy model, and the control strategy takes the form of parallel distributed compensation. The communication links existing between the plant and controller are assumed to be imperfect (that is, data packet dropouts occur intermittently, which appear typically in a network environment), and stochastic variables satisfying the Bernoulli random binary distribution are utilized to model the unreliable communication links. Attention is focused on the design of H _infin controllers such that the closed-loop system is stochastically stable and preserves a guaranteed H _infin performance. Two approaches are developed to solve this problem, based on the quadratic Lyapunov function and the basis-dependent Lyapunov function, respectively. Several examples are provided to illustrate the usefulness and applicability of the developed theoretical results.     

A Solution to the Continuous-Time ${rm H}_{infty}$ Fixed-Interval Smoother Problem

The minimum-variance fixed-interval smoother is a state-space realization of the Wiener solution generalized for time-varying problems. It involves forward and adjoint Wiener-Hopf factor inverses in which the gains are obtained by solving a Riccati equation. This technical note introduces a continuous-time ${rm H}_{infty}$ smoother having the structure of the minimum-variance version, in which the gains are obtained by solving a Riccati equation that possesses an indefinite quadratic term. It is shown that the smoother exhibits an increase in mean-square-error, the error is bounded, and the upper error bound is greater than that for the ${rm H}_{infty}$ filter.      

Piecewise $H_{infty}$ Controller Design of Uncertain Discrete-Time Fuzzy Systems With Time Delays

This paper considers the robust $H_{infty}$ control of uncertain discrete-time fuzzy systems with time delays based on piecewise Lyapunov--Krasovskii functionals. It is shown that the stability with $H_{infty}$ disturbance attenuation performance can be established for the closed-loop fuzzy control systems if there exists a piecewise Lyapunov--Krasovskii functional, and moreover, the functional and the corresponding controller can be obtained by solving a set of linear matrix inequalities that are numerically feasible. A numerical example is given to demonstrate the efficiency and the advantage of the proposed method.      

$H_{infty}$ Controller Synthesis via Switched PDC Scheme for Discrete-Time T--S Fuzzy Systems

This paper is concerned with the problem of designing switched state feedback $H_{infty}$ controllers for discrete-time Takagi--Sugeno (T--S) fuzzy systems. New types of state feedback controllers, namely, switched parallel distributed compensation (PDC) controllers, are proposed, which are switched based on the values of membership functions. Switched quadratic Lyapunov functions are exploited to derive a new method for designing switched PDC controllers to guarantee the stability and $H_{infty}$ performances of closed-loop nonlinear systems. The design conditions are given in terms of solvability of a set of linear matrix inequalities. It is shown that the new method provides better or at least the same results of the existing design methods via the pure PDC scheme with a quadratic Lyapunov function or switched constant controller gain scheme. Numerical examples are given to illustrate the effectiveness of the proposed method.      

A Parameter-Dependent Approach to Robust $H_{infty }$ Filtering for Time-Delay Systems

This paper is concerned with the problem of robust $H_{infty }$ filtering for linear continuous-time systems with polytopic parameter uncertainties and time-varying delay in the state. We utilize the polynomially parameter-dependent idea to solve the robust $H_{infty }$ filtering problem, with new linear matrix inequality conditions obtained for the existence of admissible filters. These conditions are developed based on homogeneous polynomially parameter-dependent matrices of arbitrary degree. The delay-dependence and polynomial parameter-dependence guarantee the proposed approach to be potentially less conservative, which is shown via a numerical example.      

${cal H}_{infty}$ Output-Feedback Control Based on an FIR-Type Quasi-Deadbeat Observer

This technical note proposes a novel output-feedback control law based on a finite impulse response (FIR)-type quasi-deadbeat observer for linear systems. For nominal systems without disturbances, this technical note first establishes the deadbeat condition that reduces the state estimation error to zero within a finite time and verifies that all the hidden poles of the closed-loop system under the quasi-deadbeat observer-based control law are zero and that the separation principle holds true. In order to enhance the disturbance rejection capability for systems with random-work disturbances, on the structural merit of the FIR-type observer, we have proposed the conditions for an ${cal H}_{infty}$ quasi-deadbeat observer and an ${cal H}_{infty}$ stabilizer based on the predetermined observer, respectively.      

$H_{infty}$ Filtering for Fuzzy Singularly Perturbed Systems

This paper considers the problem of designing $H_{infty}$ filters for fuzzy singularly perturbed systems with the consideration of improving the bound of singular-perturbation parameter $epsilon$. First, a linear-matrix-inequality (LMI)-based approach is presented for simultaneously designing the bound of the singularly perturbed parameter $epsilon$, and $H_{infty}$ filters for a fuzzy singularly perturbed system. When the bound of singularly perturbed parameter $epsilon$ is not under consideration, the result reduces to an LMI-based design method for $H_{infty}$ filtering of fuzzy singularly perturbed systems. Furthermore, a method is given for evaluating the upper bound of singularly perturbed parameter subject to the constraint that the considered system is to be with a prescribed $H_{infty}$ performance bound, and the upper bound can be obtained by solving a generalized eigenvalue problem. Finally, numerical examples are given to illustrate the effectiveness of the proposed methods.      

Group Interaction Analysis in Dynamic Context$^{ast}$

Computer understanding of human actions and interactions is one of the key research issues in human computing. In this regard, context plays an essential role in semantic understanding of human behavioral and social signals from sensor data. This paper put forward an event-based dynamic context model to address the problems of context awareness in the analysis of group interaction scenarios. Event-driven multilevel dynamic Bayesian network is correspondingly proposed to detect multilevel events, which underlies the context awareness mechanism. Online analysis can be achieved, which is superior over previous works. Experiments in our smart meeting room demonstrate the effectiveness of our approach.      

6H-SiC JFETs for 450 $^{circ}hbox{C}$ Differential Sensing Applications

N-channel 6H-SiC depletion-mode junction field-effect transistors (JFETs) have been fabricated, and characterized for use in high-temperature differential sensing. Electrical characteristics of the JFETs have been measured and are in good agreement with predictions of an abrupt-junction long-channel JFET model. The electrical characteristics were measured across a 2-in wafer for temperatures from 25 $^{ circ}hbox{C}$ to 450 $^{circ}hbox{C}$, and the extracted pinchoff voltage has a mean of 11.3 V and a standard deviation of about 1.0 V at room temperature, whereas pinchoff current has a mean of 0.41 mA with standard deviation of about 0.1 mA. The change in pinchoff voltage is minimal across the measured temperature range, whereas pinchoff current at 450 $^{circ}hbox{C}$ is about half its value at room temperature, consistent with the expected change in the $nmu_{n}$ product. The characterization of differential pairs and hybrid amplifiers constructed using these differential pairs is also reported. A three-stage amplifier with passive loads has a differential voltage gain of 50 dB, and a unity-gain frequency of 200 kHz at 450 $^{circ}hbox{C}$, limited by test parasitics. A two-stage amplifier with active loads has reduced sensitivity to off-chip parasitics and exhibits a differential voltage gain of 69 dB with a unity-gain frequency of 1.3 MHz at 450 $^{circ}hbox{C}$.$hfill$[2009-0029]      

Network-Based ${{cal H}}_{!!!infty }$ Output Tracking Control

This paper is concerned with the problem of H_infin output tracking for network-based control systems. The physical plant and the controller are, respectively, in continuous time and discrete time. By using a sampled-data approach, a new model based on the updating instants of the holder is formulated, and a linear matrix inequality (LMI)-based procedure is proposed for designing state-feedback controllers, which guarantee that the output of the closed-loop networked control system tracks the output of a given reference model well in the H_infin sense. Both network-induced delays and data packet dropouts have been taken into consideration in the controller design. The network-induced delays are assumed to have both an upper bound and a lower bound, which is more general than those used in the literature. The introduction of the lower bound is shown to be advantageous for reducing conservatism. Moreover, the controller design method is further extended to more general cases, where the system matrices of the physical plant contain parameter uncertainties, represented in either polytopic or norm-bounded frameworks. Finally, an illustrative example is presented to show the usefulness and effectiveness of the proposed H_infin output tracking design.     

A ${bm lambda}$-Cut and Goal-Programming-Based Algorithm for Fuzzy-Linear Multiple-Objective Bilevel Optimization

Bilevel-programming techniques are developed to handle decentralized problems with two-level decision makers, which are leaders and followers, who may have more than one objective to achieve. This paper proposes a ${lambda}$-cut and goal-programming-based algorithm to solve fuzzy-linear multiple-objective bilevel (FLMOB) decision problems. First, based on the definition of a distance measure between two fuzzy vectors using ${lambda}$-cut, a fuzzy-linear bilevel goal (FLBG) model is formatted, and related theorems are proved. Then, using a ${lambda}$-cut for fuzzy coefficients and a goal-programming strategy for multiple objectives, a ${lambda}$-cut and goal-programming-based algorithm to solve FLMOB decision problems is presented. A case study for a newsboy problem is adopted to illustrate the application and executing procedure of this algorithm. Finally, experiments are carried out to discuss and analyze the performance of this algorithm.      

Fuzzy Interpolative Reasoning for Sparse Fuzzy Rule-Based Systems Based on ${bm alpha}$-Cuts and Transformations Techniques

In sparse fuzzy rule-based systems, the fuzzy rule bases are usually incomplete. In this situation, the system may not properly perform fuzzy reasoning to get reasonable consequences. In order to overcome the drawback of sparse fuzzy rule-based systems, there is an increasing demand to develop fuzzy interpolative reasoning techniques in sparse fuzzy rule-based systems. In this paper, we present a new fuzzy interpolative reasoning method via cutting and transformation techniques for sparse fuzzy rule-based systems. It can produce more reasonable results than the existing methods. The proposed method provides a useful way to deal with fuzzy interpolative reasoning in sparse fuzzy rule-based systems.