$ {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.      

Reflection Coefficients of Polynomials and Stable Polytopes

The geometry of stable discrete polynomials using their coefficients and reflection coefficients is investigated. Two linear Schur invariant transformations with a free parameter in the polynomial coefficient space are introduced. The first transformation ${cal R}^{n}times{cal R}rightarrow{cal R}^{n}$ maps an arbitrary stable polytope into another stable polytope. The second transformation ${cal R}^{n}times{cal R}rightarrow{cal R}^{n+1}$ maps a stable tilted $n$-dimensional hyperrectangle defined by the discrete Kharitonov theorem into a stable $(n+1)$- dimensional polytope.      

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]      

Exponential Stability on Stochastic Neural Networks With Discrete Interval and Distributed Delays

This brief addresses the stability analysis problem for stochastic neural networks (SNNs) with discrete interval and distributed time-varying delays. The interval time-varying delay is assumed to satisfy $0≪d_{1}leq d(t) leq d_{2}$ and is described as $d(t)= d_{1}+h(t)$ with $0leq h(t) leq d_{2}-d_{1}$. Based on the idea of partitioning the lower bound $d_{1}$, new delay-dependent stability criteria are presented by constructing a novel Lyapunov–Krasovskii functional, which can guarantee the new stability conditions to be less conservative than those in the literature. The obtained results are formulated in the form of linear matrix inequalities (LMIs). Numerical examples are provided to illustrate the effectiveness and less conservatism of the developed results.      

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.      

Exponentially Stable Nonlinear Systems Have Polynomial Lyapunov Functions on Bounded Regions

This paper presents a proof that existence of a polynomial Lyapunov function is necessary and sufficient for exponential stability of a sufficiently smooth nonlinear vector field on a bounded set. The main result states that if there exists an $n$ -times continuously differentiable Lyapunov function which proves exponential stability on a bounded subset of $ BBR ^{n}$, then there exists a polynomial Lyapunov function which proves exponential stability on the same region. Such a continuous Lyapunov function will exist if, for example, the vector field is at least $n$-times continuously differentiable. The proof is based on a generalization of the Weierstrass approximation theorem to differentiable functions in several variables. Specifically, polynomials can be used to approximate a differentiable function, using the Sobolev norm $W^{1,infty }$ to any desired accuracy. This approximation result is combined with the second-order Taylor series expansion to show that polynomial Lyapunov functions can approximate continuous Lyapunov functions arbitrarily well on bounded sets. The investigation is motivated by the use of polynomial optimization algorithms to construct polynomial Lyapunov functions.      

A Necessary and Sufficient Frequency Domain Criterion for the Passivity of SISO Sampled-Data Systems

We present a frequency domain solution to the sampled-data passivity problem. Our analysis is exact in the sense that we take into account the intersample behavior of the system. We use frequency response (FR) operators to first obtain necessary conditions on the sampling rate $T$ and the relative degree of the open-loop transfer function $G_{11}$ for achieving a passive continuous-time closed-loop system. Then, assuming passivity of $G_{11}$ and closed-loop stability, we derive a necessary and sufficient condition for discrete-time controllers that render a passive closed-loop system. We apply the obtained results to the problem of stability of haptic systems.      

Cryogenic Etching of Silicon: An Alternative Method for Fabrication of Vertical Microcantilever Master Molds

This paper examines the use of deep reactive ion etching of silicon with fluorine high-density plasmas at cryogenic temperatures to produce silicon master molds for vertical microcantilever arrays used for controlling substrate stiffness for culturing living cells. The resultant profiles achieved depend on the rate of deposition and etching of an $hbox{SiO}_{x}hbox{F}_{y}$ polymer, which serves as a passivation layer on the sidewalls of the etched structures in relation to areas that have not been passivated with the polymer. We look at how optimal tuning of two parameters, the $ hbox{O}_{2}$ flow rate and the capacitively coupled plasma power, determine the etch profile. All other pertinent parameters are kept constant. We examine the etch profiles produced using electron-beam resist as the main etch mask, with holes having diameters of 750 nm, 1 $muhbox{m}$ , and 2 $muhbox{m}$. $hfill$[2008-0317]      

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]      

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.      

Design, Modeling, and Fabrication of MEMS-Based Multicapillary Gas Chromatographic Columns

This paper describes different approaches to achieve high-performance microfabricated silicon-glass separation columns for microgas chromatography systems. The capillary width effect on the separation performance has been studied by characterization of 250-, 125-, 50-, and 25-$muhbox{m}$ -wide single-capillary columns (SCCs) fabricated on a $10 times 8 hbox{mm}^{2}$ die. The highest plate number (12 500/m), reported to date for MEMS-based silicon-glass columns, has been achieved by 25-$muhbox{m}$-wide columns coated by a thin layer of polydimethylsiloxane stationary phase using static coating technique. To address the low sample capacity of these narrow columns, this paper presents the first generation of MEMS-based “multicapillary” columns (MCCs) consisting of a bundle of narrow-width rectangular capillaries working in parallel. The theoretical model for the height-equivalent-to-a-theoretical-plate $(HETP)$ of rectangular MCCs has been developed, which relates the $HETP$ to the discrepancies of the widths and depths of the capillaries in the bundle. Two-, four-, and eight-capillary MCCs have been designed and fabricated to justify the separation ability of these columns. These MCCs capable of multicomponent gas separation provide a sample capacity as large as 200 ng compared to 5.5 ng for 25-$muhbox{m}$-wide SCCs.$hfillhbox{[2007-0309]}$      

Performance Recovery of Feedback-Linearization-Based Designs

We consider a tracking problem for a partially feedback linearizable nonlinear system with stable zero dynamics. The system is uncertain and only the output is measured. We use an extended high-gain observer of dimension $n+1$, where $n$ is the relative degree. The observer estimates $n$ derivatives of the tracking error, of which the first $(n-1)$ derivatives are states of the plant in the normal form and the $n$th derivative estimates the perturbation due to model uncertainty and disturbance. The controller cancels the perturbation estimate and implements a feedback control law, designed for the nominal linear model that would have been obtained by feedback linearization had all the nonlinearities been known and the signals been available. We prove that the closed-loop system under the observer-based controller recovers the performance of the nominal linear model as the observer gain becomes sufficiently high. Moreover, we prove that the controller has an integral action property in that it ensures regulation of the tracking error to zero in the presence of constant nonvanishing perturbation.      

Tungsten-Based SOI Microhotplates for Smart Gas Sensors

This paper is concerned with the design, fabrication, and characterization of novel high-temperature silicon on insulator (SOI) microhotplates employing tungsten resistive heaters. Tungsten has a high operating temperature and good mechanical strength and is used as an interconnect in high temperature SOI-CMOS processes. These devices have been fabricated using a commercial SOI-CMOS process followed by a deep reactive ion etching (DRIE) back-etch step, offering low cost and circuit integration. In this paper, we report on the design of microhotplates with different diameters (560 and 300 $muhbox{m}$) together with 3-D electrothermal simulation in ANSYS, electrothermal characterization, and analytical analysis. Results show that these devices can operate at high temperatures (600 $^{circ}hbox{C}$ ) well beyond the typical junction temperatures of high temperature SOI ICs (225 $^{circ}hbox{C}$), have ultralow dc power consumption (12 mW at 600 $^{circ}hbox{C}$), fast transient time (as low as 2-ms rise time to 600 $^{circ}hbox{C}$), good thermal stability, and, more importantly, a high reproducibility both within a wafer and from wafer to wafer. We also report initial tests on the long-term stability of the tungsten heaters. We believe that this type of SOI microhotplate could be exploited commercially in fully integrated microcalorimetric or resistive gas sensors. $hfill$[2007-0275]      

A Laterally Movable Gate Field Effect Transistor

A laterally movable gate field effect transistor (LMGFET) device that directly couples lateral mechanical gate motion to drain current of a FET is presented in this paper. Lateral motion of the FET gate results in a change in channel width, keeping the channel length and the gap between the gate and the oxide layer constant. This results in a change in channel current that, in principle, is linearly proportional to mechanical motion. The operating principle of an LMGFET, along with details of the fabrication process for a depletion-type LMGFET device, is described. Fabricated LMGFET shows an average drain current sensitivity to gate motion of $-5.8 muhbox{A}/muhbox{m}$ at $V_{rm DS} = 20 hbox{V}$ and $V_{rm GS} = 0 hbox{V}$ for 60-$muhbox{m}$ gate motion. A model for the fabricated LMGFET is developed based on electrical measurements. The device shows promise both as a sensor and as an actuator in MEMS and other related applications.$hfill$ [2008-0147]      

Thermal Degradation of Electroplated Nickel Thermal Microactuators

In this paper, the thermal degradation of laterally operating thermal actuators made from electroplated nickel has been studied. The actuators investigated delivered a maximum displacement of ca. 20 $muhbox{m}$ at an average temperature of $sim!! 450 ,^{circ}hbox{C}$ , which is much lower than that of typical silicon-based microactuators. However, the magnitude of the displacement strongly depended on the frequency and voltage amplitude of the pulse signal applied. Back bending was observed at maximum temperatures as low as 240 $^{circ}hbox{C}$. Both forward and backward displacements increase as the applied power was increased up to a value of 60 mW; further increases led to reductions in the magnitudes of both displacements. Scanning electron microscopy clearly showed that the nickel beams began to deform and change their shape at this critical power level. Compressive stress is responsible for nickel pileup, while tensile stresses, generated upon removing the current, are responsible for necking at the hottest section of the hot arm of the device. Energy dispersive X-ray diffraction analysis also revealed the severe oxidation of Ni structure induced by Joule heating. The combination of plastic deformation and oxidation was responsible for the observed thermal degradation. Results indicate that nickel thermal microactuators should be operated below 200 $^{circ}hbox{C}$ to avoid thermal degradation.$hfill$[2009-0015]      

Relaxed Conditions for the Exponential Stability of a Class of Linear Time-Varying Systems

This technical note states new sufficient conditions for the exponential stability of linear time-varying (LTV) systems of the form $mathdot{x}(cdot)=A(t)x(t)$. The approach proposed derives and uses the notion of perturbed frozen time (PFT) form that can be associated to any LTV system. Exploiting the Bellman-Gronwall lemma, relaxed stability conditions are then stated in terms of “average” parameter variations. Salient features of the approach are: pointwise stability of $A(cdot)$ is not required, $Vertmathdot{A}(cdot)Vert$ may not be bounded, the stability conditions also apply to uncertain systems. The approach is illustrated by numerical examples.      

High-Voltage Dielectrophoretic and Magnetophoretic Hybrid Integrated Circuit/Microfluidic Chip

A hybrid integrated circuit (IC)/microfluidic chip is presented that independently and simultaneously traps and moves microscopic objects suspended in fluid using both electric and magnetic fields. This hybrid chip controls the location of dielectric objects, such as living cells and drops of fluid, on a 60 $times$ 61 array of pixels that are $30 times 38 mu hbox{m}^{2}$ in size, each of which can be individually addressed with a 50-V peak-to-peak dc-to-10-MHz radio-frequency voltage. These high-voltage pixels produce electric fields above the chip's surface with a magnitude $vert vec{E}vert approx 1 hbox{V}/muhbox{m}$ , resulting in strong dielectrophoresis (DEP) forces $vert vec{F}_{ rm DEP}vert approx 1 hbox{nN}$. Underneath the array of DEP pixels, there is a magnetic matrix that consists of two perpendicular sets of 60 metal wires running across the chip. Each wire can be sourced with 120 mA to trap and move magnetically susceptible objects using magnetophoresis. The DEP pixel array and magnetic matrix can be used simultaneously to apply forces to microscopic objects, such as living cells or lipid vesicles, that are tagged with magnetic nanoparticles. The capabilities of the hybrid IC/microfluidic chip demonstrated in this paper provide important building blocks for a platform for biological and chemical applications. $hfill$[2009-0142]      

Neurodynamic Programming and Zero-Sum Games for Constrained Control Systems

In this paper, neural networks are used along with two-player policy iterations to solve for the feedback strategies of a continuous-time zero-sum game that appears in $L_{2}$ -gain optimal control, suboptimal $H_{infty}$ control, of nonlinear systems affine in input with the control policy having saturation constraints. The result is a closed-form representation, on a prescribed compact set chosen a priori, of the feedback strategies and the value function that solves the associated Hamilton–Jacobi–Isaacs (HJI) equation. The closed-loop stability, $L_{2}$-gain disturbance attenuation of the neural network saturated control feedback strategy, and uniform convergence results are proven. Finally, this approach is applied to the rotational/translational actuator (RTAC) nonlinear benchmark problem under actuator saturation, offering guaranteed stability and disturbance attenuation.      

A Fast Liquid-Metal Droplet Microswitch Using EWOD-Driven Contact-Line Sliding

Liquid-metal (LM) droplet-based MEMS switches have mostly been restricted to slow applications until now due to the following reasons: 1) a relatively large switching gap (distance) needed to accommodate imprecise volumes and locations of droplets on the device and 2) lack of high-speed actuation to move the droplets quickly across the switching gap. To combat these problems, we explore switching by sliding the solid–LM–gas triple contact line rather than the entire droplet. This new approach allows us to use a microframe, which not only consistently positions the LM droplet but also makes the switching gap less sensitive to the errors in the deposited-droplet volume, allowing us to design microswitches with very small switching gaps (e.g., 10 $muhbox{m}$ for 600 $muhbox{m}$-diameter droplets). Furthermore, a study of electrowetting-on-dielectric identifies a regime of fast contact-line sliding at the onset of droplet spreading. By moving the contact line fast across a small switching distance, we demonstrate a low-latency LM switch with 60 $muhbox{s}$ switch-on latency ( $sim$20 times better than other LM-switch technologies) and better than 5 $muhbox{s}$ signal rise/fall time, while boasting no contact bounce, as expected from an LM switch. High power-handling capability and long-term reliability are also discussed. $hfill$[2008-0135]      

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]