Fuzzy Subsethood for Fuzzy Sets of Type-2 and Generalized Type- ${n}$

In this paper, we use Zadeh's extension principle to extend Kosko's definition of the fuzzy subsethood measure $S(G,H)$ to type-2 fuzzy sets defined on any set $X$ equipped with a measure. Subsethood is itself a fuzzy set that is a crisp interval when $G$ and $H$ are interval type-2 sets. We show how to compute this interval and then use the result to compute subsethood for general type-2 fuzzy sets. A definition of subsethood for arbitrary fuzzy sets of type- $n ≫ 2$ is then developed. This subsethood is a type-( $n-1$) fuzzy set, and we provide a procedure to compute subsethood of interval type-3 fuzzy sets.      

How to Make $T$-Transitive a Proximity Relation

Three ways to approximate a proximity relation $R$ (i.e., a reflexive and symmetric fuzzy relation) by a $T$ -transitive one where $T$ is a continuous Archimedean $t$-norm are given. The first one aggregates the transitive closure $overline{R}$ of $R$ with a (maximal) $T$-transitive relation $B$ contained in $R$ . The second one computes the closest homotecy of $overline{R}$ or $B$ to better fit their entries with the ones of $R$. The third method uses nonlinear programming techniques to obtain the best approximation with respect to the Euclidean distance for $T$ the $Lstrok$ukasiewicz or the product $t$-norm. The previous methods do not apply for the minimum $t$-norm. An algorithm to approximate a given proximity relation by a ${rm Min}$-transitive relation (a similarity) is given in the last section of the paper.      

On the NP-Hardness of Checking Matrix Polytope Stability and Continuous-Time Switching Stability

Motivated by questions in robust control and switched linear dynamical systems, we consider the problem checking whether all convex combinations of $k$ matrices in $R^{n times n}$ are stable. In particular, we are interested whether there exist algorithms which can solve this problem in time polynomial in $n$ and $k$. We show that if $k= lceil n^{d} rceil $ for any fixed real $d>0$, then the problem is NP-hard, meaning that no polynomial-time algorithm in $n$ exists provided that $P ne NP$, a widely believed conjecture in computer science. On the other hand, when $k$ is a constant independent of $n$ , then it is known that the problem may be solved in polynomial time in $n$. Using these results and the method of measurable switching rules, we prove our main statement: verifying the absolute asymptotic stability of a continuous-time switched linear system with more than $n^{d}$ matrices $A_{i} in R^{n times n}$ satisfying $0 succeq A_{i} + A_{i}^{T}$ is NP-hard.      

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.      

On Constructing Parsimonious Type-2 Fuzzy Logic Systems via Influential Rule Selection

Type-2 fuzzy systems are increasing in popularity, and there are many examples of successful applications. While many techniques have been proposed for creating parsimonious type-1 fuzzy systems, there is a lack of such techniques for type-2 systems. The essential problem is to reduce the number of rules, while maintaining the system's approximation performance. In this paper, four novel indexes for ranking the relative contribution of type-2 fuzzy rules are proposed, which are termed $R$-values, $c$-values, $omega _1 $-values, and $omega _2 $-values. The $R$-values of type-2 fuzzy rules are obtained by applying a QR decomposition pivoting algorithm to the firing strength matrices of the trained fuzzy model. The $c$-values rank rules based on the effects of rule consequents, while the $omega _1 $-values and $omega _2 $-values consider both the rule-base structure (via firing strength matrices) and the output contribution of fuzzy rule consequents. Two procedures for utilizing these indexes in fuzzy rule selection (termed “forward selection” and “backward elimination”) are described. Experiments are presented which demonstrate that by using the proposed methodology, the most influential type-2 fuzzy rules can be effectively retained in order to construct parsimonious type-2 fuzzy models.      

Reducing Anchor Loss in MEMS Resonators Using Mesa Isolation

In microelectromechanical systems resonators, dissipation of energy through anchor points into the substrate adds to resonator energy loss, contributing to low values of $Q$. A design for improving $Q$ based on the reflection of anchor-generated surface acoustic waves is presented here. In this design, the resonator is surrounded by a trench, or a mesa, that partially reflects the wave energy back to the resonator. Depending on the distance from the resonator to the mesa, the reflected wave interferes either constructively or destructively with the resonator, increasing or decreasing $Q$. The proposed design is experimentally tested using a dome-shaped flexural mode resonator for a range of distances of the mesa from the resonator. Improvements in $Q$ of up to 400% are observed. The resonator/mesa system is modeled using a commercially available finite-element code. Experiments and simulations compare well, suggesting that a finite-element-method analysis can be used in the preliminary design of mesas for the optimization of $Q$. The concept of using mesas to improve $Q$ is simulated for both flexural and in-plane modes of vibration.$hfill$[2008-0149]      

Analytical Model of Valveless Micropumps

The flow driven by a valveless micropump with a single cylindrical pump chamber and two diffuser/nozzle elements is studied theoretically using a 1-D model. The pump cavity is driven at an angular frequency $omega$ so that its volume oscillates with an amplitude $V_{rm m}$. The presence of diffuser/nozzle elements with pressure-drop coefficients $zeta_{+}$, $zeta_{-}( ≫ zeta_{+})$ and throat cross-sectional area $A_{1}$ creates a rectified mean flow. In the absence of frictional forces the maximum mean volume flux (with zero pressure head) is $Q_{0}$ where $Q_{0}/V_{rm m}omega = (zeta_{-} -break zeta_{+})pi/16(zeta_{-}+zeta_{+})$, while the maximum pressure that can be overcome is $Delta P_{max}$ where $ Delta P_{max}A_{1}^{2}/V_{rm m}^{2} omega^{2} !=! (zeta_{-} -break zeta_{+})/16$. These analytical results agree with numerical calculations for the coupled system of equations and compare well with the experimental results of Stemme and Stemme.$hfill$ [2008-0244]      

$ {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.      

Serially Connected Weight-Balanced Digital Actuators for Wide-Range High-Precision Low-Voltage-Displacement Control

This paper presents the design, fabrication, and characterization of a new serial digital actuator, achieving an improvement in range-to-precision and range-to-voltage performance. We propose a weight-balanced design for the serial actuators with serpentine springs with a serial arrangement of unit digital actuators. We have measured the displacement range, precision, and drive voltage of unit and serial actuation at 1 Hz. The serial digital actuators produce a full-range displacement of $28.44 pm 0.02 muhbox{m}$ , accumulating unit displacements of $2.8 pm 0.5 muhbox{m}$ at an operating voltage of 4.47 $pm$ 0.07 V. In addition, the serial digital actuators that have a displacement precision of 37.94 $pm$ 6.26 nm do not accumulate the displacement errors of the unit actuators, i.e., 36.0 $pm$ 17.7 nm. We experimentally verify that the serial digital actuators achieve a range-to-squared-voltage ratio of 1.423 $muhbox{m/V}^{2}$ and a range-to-precision ratio of 749.6.$hfill$ [2009-0020]      

A Programmable Array for Contact-Free Manipulation of Floating Droplets on Featureless Substrates by the Modulation of Surface Tension

This paper presents a contactless droplet manipulation system that relies on thermally generated Marangoni flows. Programmable 2-D control of aqueous microdroplets suspended in an oil film on a plain featureless glass substrate is achieved using a 128-pixel heater array suspended 100–500 $mu hbox{m}$ above the oil layer. The heaters generate surface temperature perturbations $(≪ 25 ^{circ}hbox{C})$, resulting in local Marangoni flows that can move droplets in either a push or a pull mode. Programmed movement is achieved by the sequential activation of the heaters, with digital control circuitry and a graphical interface providing addressable control of each heater. Droplets with diameters of 300–1000 $muhbox{m}$ are manipulated and merged at speeds up to 140 $muhbox{m/s}$. Evaporation rates can be reduced by almost two orders of magnitude by using a two-layer-oil medium, and the choice of an optimum carrier fluid can achieve fluid velocities over 17 000 $mu hbox{m/s}$. The system provides a contactless platform for parallel droplet-based assays. As such, it circumvents the challenges of sample contamination and loss that occur when a droplet interacts with a solid surface.$hfill$[2008-0272]      

Real-Time Temperature Compensation of MEMS Oscillators Using an Integrated Micro-Oven and a Phase-Locked Loop

We present a new temperature compensation system for microresonator-based frequency references. It consists of a phase-locked loop (PLL) whose inputs are derived from two microresonators with different temperature coefficients of frequency. The resonators are suspended within an encapsulated cavity and are heated to a constant temperature by the PLL controller, thereby achieving active temperature compensation. We show repeated real-time measurements of three 1.2-MHz prototypes that achieve a frequency stability of $pm$ 1 ppm from $-20 ^{circ}hbox{C}$ to $+80 ^{circ}hbox{C}$, as well as a technique to reduce steady-state frequency errors to $pm$0.05 ppm using multipoint calibration.$hfill$[2009-0074]      

Discharge-Based Pressure Sensors for High-Temperature Applications Using Three-Dimensional and Planar Microstructures

Two versions of microdischarge-based pressure sensors, which operate by measuring the change, with pressure, in the spatial current distribution of pulsed dc microdischarges, are reported. The inherently high temperatures of the ions and electrons in the microdischarges make these devices amenable to high-temperature operation. The first sensor type uses 3-D arrays of horizontal bulk metal electrodes embedded in quartz substrates with electrode diameters of 1–2 mm and 50–100-$muhbox{m}$ interelectrode spacing. These devices were operated in nitrogen over a range of 10–2000 torr, at temperatures as high as 1000 $^{circ}hbox{C}$. The maximum measured sensitivity was 5420 ppm/torr at the low end of the dynamic range and 500 ppm/torr at the high end, while the temperature coefficient of sensitivity ranged from $-$925 to $-$550 ppm/K. Sensors of the second type use planar electrodes and have active areas as small as 0.13 $hbox{mm}^{2}$. These devices, when tested in a chemical sensing system flowing helium as a carrier gas, had a maximum sensitivity of 9800 ppm/torr, a dynamic range of 25–200 torr, and a temperature coefficient of sensitivity of approximately $-$1412 ppm/K.$hfill$ [2008-0262]      

Evanescent-Wave Spectroscopy Using an SU-8 Waveguide for Rapid Quantitative Detection of Biomolecules

A 30-mm-long multimode waveguide, 40 $muhbox{m}$ wide and 40 $muhbox{m}$ high, is fabricated on a silicon wafer using polymer SU-8 as the core and liquid buffer as the cladding. Antibodies are successfully immobilized on the SU-8 surface designated for binding target antigens dispersed in the buffer solution. Evanescent-wave spectroscopy is performed by exciting the fluorescently labeled antigens, bound to the waveguide surface within its evanescence field, and measuring the emission light intensity. This evanescent-wave biosensor detects specific molecular interaction. The optical output as a function of the antigen concentration can be described by Langmuir equation. Antigen concentration as low as 1.5 $muhbox{g}/hbox{mL}$ is detected; concentrations higher than 100 $muhbox{g}/hbox{mL}$ lead to sensor saturation. $hfill$[2008-0058]      

${cal H}_{infty}$ State-Feedback Control Design for Fuzzy Systems Using Lyapunov Functions With Quadratic Dependence on Fuzzy Weighting Functions

This paper proposes a method for designing an ${cal H}_{infty}$ state-feedback fuzzy controller for discrete-time Takagi–Sugeno (T-S) fuzzy systems. To derive less conservative ${cal H}_{infty}$ stabilization conditions, this paper enhances the interactions among the fuzzy subsystems using a multiple Lyapunov function with quadratic dependence on fuzzy weighting functions. Besides, for more allocation of the nonlinearity to the fuzzy control system, this paper introduces a slack variable that is quadratically dependent on the one-step-past fuzzy weighting functions as well as the current ones. In the derivation, the ${cal H}_{infty}$ stabilization conditions are formulated in terms of parameterized linear matrix inequalities (PLMIs), which are reconverted into LMI conditions with the help of an efficient relaxation technique.      

Distance-Dependent Head-Related Transfer Functions Measured With High Spatial Resolution Using a Spark Gap

A measurement of head-related transfer functions (HRTFs) with high spatial resolution was carried out in this study. HRTF measurement is difficult in the proximal region because of the lack of an appropriate acoustic point source. In this paper, a modified spark gap was used as the acoustic sound source. Our evaluation experiments showed that the spark gap was more like an acoustic point source than others previously used from the viewpoints of frequency response, directivity, power attenuation, and stability. Using this spark gap, high spatial resolution HRTFs were measured at 6344 spatial points, with distances from 20 to 160 cm, elevations from $-$40$^circ$ to 90 $^circ$, and azimuths from 0$^circ$ to 360$^circ$. Based on these measurements, an HRTF database was obtained and its reliability was confirmed by both objective and subjective evaluations.      

Binaural Sound Source Distance Learning in Rooms

A method for learning the distance of a sound source in a room is presented. The proposed method is based on short-time magnitude-squared coherence between the two channels of a binaural signal. Based on white noise as the training data, a coherence profile is obtained at each desired position in the room. These profiles can then be used to identify the most likely distance of a speech signal in the same room. The proposed approach is compared to a previous method for learning the position of a sound source. The results indicate that the both methods are able to identify the distance of a speech sound source correctly in a grid with 0.5-m spacing in most cases, when the orientation of the listener is 0$^{circ}$ , 30$^{circ}$ , 60$^{circ}$ , 90$^{circ}$ , or 180$^{circ}$ on the horizontal plane.      

A Separation Principle for Linear Switching Systems and Parametrization of All Stabilizing Controllers

In this paper, we investigate the problem of designing a switching compensator for a plant switching amongst a (finite) family of given configurations $(A_{i},B_{i},C_{i})$. We assume that switching is uncontrolled, namely governed by some arbitrary switching rule, and that the controller has the information of the current configuration $i$ .      

Post-CMOS-Compatible Aluminum Nitride Resonant MEMS Accelerometers

This paper describes the development of aluminum nitride (AlN) resonant accelerometers that can be integrated directly over foundry CMOS circuitry. Acceleration is measured by a change in resonant frequency of AlN double-ended tuning-fork (DETF) resonators. The DETF resonators and an attached proof mass are composed of a 1- $muhbox{m}$ -thick piezoelectric AlN layer. Utilizing piezoelectric coupling for the resonator drive and sense, DETFs at 890 kHz have been realized with quality factors $(Q)$ of 5090 and a maximum power handling of 1 $muhbox{W}$. The linear drive of the piezoelectric coupling reduces upconversion of $1/f$ amplifier noise into $1/f^{3}$ phase noise close to the oscillator carrier. This results in lower oscillator phase noise, $-$96 dBc/Hz at 100-Hz offset from the carrier, and improved sensor resolution when the DETF resonators are oscillated by the readout electronics. Attached to a 110-ng proof mass, the accelerometer microsystem has a measured sensitivity of 3.4 Hz/G and a resolution of 0.9 $hbox{mG}/surdhbox{Hz}$ from 10 to 200 Hz, where the accelerometer bandwidth is limited by the measurement setup. Theoretical calculations predict an upper limit on the accelerometer bandwidth of 1.4 kHz.$hfill$ [2008-0190]      

Controlled Thermophoresis as an Actuation Mechanism for Noncantilevered MEMS Devices

A microelectromechanical system actuator based on thermophoretic, or Knudson, forces is proposed using analytical calculations. It can potentially execute scanning or spinning motions of a body that is not mechanically attached to the reference substrate. For a silicon device of 100-$muhbox{m}$ diameter, it is calculated that it can be levitated at a distance of about 0.5 $muhbox{m}$ from a substrate and that it can execute scanning motion and use quasi-springs by laterally acting thermal forces. In this way, an engine with spinning motion of a floating body having a diameter of 200 $muhbox{m}$ with up to 5 kHz can be achieved.$hfill$[2008-0013]      

Wireless Magnetoelastic Monitoring of Biliary Stents

This paper presents a system for wirelessly monitoring the accumulation of sludge in a biliary stent. Two generations of the system are detailed. The first-generation system utilizes a 2 $times$ 37.5-mm ribbon sensor with a mass of 18 mg, along with 0.8-mm-thick $times$ 1.6-mm-diameter neodymium magnets to bias the sensor. Both components are integrated with a 4-mm-diameter stainless steel stent. The second-generation system comprises a sensor and a magnetic layer [consisting of strontium ferrite particles suspended in polydimethylsiloxane (PDMS)] that conform to the meshed topology and tubular curvature of a 5-mm-diameter Elgiloy stent. The second-generation sensors have an active area of 7.5 $times$ 29 mm and a mass of 9.1 mg. The sensors in both generations are fabricated from 28-$muhbox{m}$ -thick foils of magnetoelastic 2826MB Metglas, an amorphous Ni–Fe alloy. Analytical and finite-element models that predict sensor response in the dynamic biological environment are presented. The response of each system to viscosity changes that precede and accompany biliary sludge accumulation is tested, with resonant frequency changes of 2.8% and 6.5% over a 10-cP range for each respective generation. Sludge accumulation is simulated with successive coatings of either paraffin or an acrylate terpolymer. Resonant frequency response to this mass loading effect is similar for both generations of the system, showing a 40% decrease after applying a mass load of 2.5$times$ the mass of the sensor. $hfill$[2008-0154]