$ {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.      

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.      

${cal H}_{infty}$ 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.      

${cal H}_{infty}$ 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.      

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.      

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]      

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.      

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.      

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.      

Stability Margins of Adaptive Control Architecture

This technical note presents the ${cal L}_{1}$ adaptive control architecture for systems in the presence of unknown high-frequency gain with known sign, time-varying unknown parameters and disturbances. The ${cal L}_{1}$ adaptive controller leads to uniform performance bounds for the system's input and output signals, which can be systematically improved by increasing the adaptation rate. For constant unknown parameters, this result leads to analytically computable time-delay margin of a semiglobal nature.      

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.      

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]      

A Novel Micromachining Process Using DRIE, Thermal Oxidation, Electroplating, and Planarization to Create High Aspect Ratio Coplanar Waveguides

A micromachining process has been developed to create high aspect ratio coplanar waveguides (HARCs). The process creates tall Si mesas using deep reactive-ion etching and converts them into solid $hbox{SiO}_{2}$ mesas using thermal oxidation. Tall Au conductors are deposited using electroplating and planarized using lapping and chemical-mechanical planarization. The solid $hbox{SiO}_{2}$ mesas form the dielectric gap between the tall Au conductors, resulting in HARCs with a planar surface. The tall conductor sidewalls created from the high aspect ratio process reduce the transmission line resistance, which allows the lines to have lower loss at low impedances compared to conventional transmission lines. Transmission lines with characteristic impedances of 16–21 $Omega$ have been fabricated on high-resistivity Si. Transmission line characteristics were measured from 1 to 50 GHz and showed an attenuation of 1.0–1.4 dB/cm at 10 GHz. Measurements were compared to HFSS simulations and showed reasonable agreement over the frequency range. $hfill$[2009-0132]      

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.      

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.      

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.      

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]      

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]      

Two-Dimensional Contact and Noncontact Micromanipulation in Liquid Using an Untethered Mobile Magnetic Microrobot

This paper presents the manipulation of microspheres under water by use of an untethered electromagnetically actuated magnetic microrobot (Mag-$mu$Bot), with dimensions $hbox{250} times hbox{130} times hbox{100} mu$ m$^3$. Manipulation is achieved by two means: contact and noncontact pushing modes. In contact manipulation, the Mag-$mu$Bot is used to physically push the microspheres. In noncontact manipulation, the fluid flow generated by the translation of the Mag-$mu$Bot is used to push the microspheres. Modeling of the system is performed, taking into account micrometer-scale surface forces and fluid drag effects to determine the motion of a sphere within a robot-generated fluid flow. Fluid drag models for free-stream flow and formulations for near-wall flow are both analyzed and compared with the experiments, in which pushing of two sphere sizes, i.e., $hbox{50}$ and $hbox{230}, mu$m diameters, is characterized in a controlled, robot-generated flow. Dynamic simulations are provided using the developed physical models to capture this behavior. We find that the near-wall physical models are, in general, in agreement with the experiment, and free-stream models overestimate microsphere motion.