L2-Stability Of A Class Of Nonlinear-Systems

Sufficient conditions are given for the L2-stability of a class of feedback systems consisting of a linear operator G and a nonlinear gain function, either odd monotone or restricted by a power-law, in cascade, in a negative feedback loop. The criterion takes the form of a frequency-domain inequality, Re[1 + Z(jω)] G(jω) δ > 0 ω ε (−∞, +∞), where Z(jω) is given by, Z(jω) = β[Y1(jω) + Y2(jω)] + (1 − β)[Y3(jω) − Y3(−jω)], with 0 β 1 and the functions y1(·), y2(·) and y3(·) satisfying the time-domain inequalities, ∝−∞+∞¦y1(t) + y2(t)¦ dt 1 − ε, y1(·) = 0, t < 0, y2(·) = 0, t > 0 and ε > 0, and , c2 being a constant depending on the order of the power-law restricting the nonlinear function. The criterion is derived using Zames' passive operator theory and is shown to be more general than the existing criteria

Time-Domain Criteria For L2-Stability Of Nonstationary Feedback-Systems

Criteria for the L2-stability of linear and nonlinear time-varying feedback systems are given. These are conditions in the time domain involving the solution of certain associated matrix Riccati equations and permitting the use of a very general class of L2-operators as multipliers.

Rare earth exchanged (Ce3+, La3+ and RE3+) H-Y zeolites as solid acid catalysts for the synthesis of linear alkyl benzenes

Rare earth exchanged H–Y zeolites were prepared by simple ion exchange methods at 353 K and have been characterized using different physicochemical techniques. A strong peak around 58 ppm in the 27Al{1H} MAS NMR spectra of these zeolites suggests a tetrahedral coordination for the framework aluminium. Small peak at or near 0 ppm is due to hexa-coordinated extra-framework aluminium and a shoulder peak near 30 ppm is a penta-coordinated aluminium species; [Al(OH)4]−. The vapor-phase benzene alkylation with 1-decene and 1-dodecene was investigated with these catalytic systems. Under the reaction conditions of 448 K, benzene/olefin molar ratio of 20 and time on stream 3 h, the most efficient catalyst was CeH–Y which showed more than 70% of olefin conversion with 48.5% 2-phenyldecane and 46.8%, 2-phenyldodecane selectivities with 1-decene and 1-dodecene respectively.

Chemical Aspects of the Synergistic Hypergolic Ignition in Hybrid Systems with N2O4 as Oxidizer

Synergistic hypergolic ignition with nitrogen tetroxide ( N2O4) as oxidizer has been observed in hybrid systems comprising of a mixture of magnesium and Schiff bases as fuels. The ignition delays (IDs) measured using a modified device, have been compared with those of magnesium-Schiff base-WFNA systems under identical conditions. The ID has been found to vary with the nature of the substitution in both the benzene rings. A linear relationship emerges when the ignition delays are plotted against the Hammett substitution constants (σ). The preignition products of the reaction of N2O4 with magnesium and benzylidineaniline have been analysed to be Mg(NO3)2, benzenediazonium salt and benzaldehyde. Based on the preignition products isolated, a probable reaction mechanism has been proposed. The previously proposed preignition mechanism for the Schiff base-magnesium-WFNA system has been further supported from the present ignition delay data.

Non-linear Dynamic Analysis of a Piezoelectrically Actuated Flapping Wing

An energy method is used in order to derive the non-linear equations of motion of a smart flapping wing. Flapping wing is actuated from the root by a PZT unimorph in the piezofan configuration. Dynamic characteristics of the wing, having the same size as dragonfly Aeshna Multicolor, are analyzed using numerical simulations. It is shown that flapping angle variations of the smart flapping wing are similar to the actual dragonfly wing for a specific feasible voltage. An unsteady aerodynamic model based on modified strip theory is used to obtain the aerodynamic forces. It is found that the smart wing generates sufficient lift to support its own weight and carry a small payload. It is therefore a potential candidate for flapping wing of micro air vehicles.

MNDO study of coupled strained hydrocarbons: Additivity of exocyclic C---C bond contraction induced by different ring systems

MNDO geometry optimizations were carried out on a series of symmetrically and unsymmetrically coupled strained ring hydrocarbons, R1-R1 and R1–R2 (R1=methyl, cyclopropyl, 1-bicyclo[1.1.0]butyl, 1-bicyclo[1.1.1]pentyl, prismyl, cubyl, 6-tricyclo [3.1.1.03,6]heptyl, and tetrahedryl groups; R2=methyl and cyclopropyl). The remarkable contraction of the C---C bond connecting the strained rings found experimentally in a few cases was reproduced correctly by the calculations. A linear correlation was found between the bond length shortening and the bond angle widening at the corresponding carbon atoms for all the structures considered. The reduction in C---C bond lengths due to various ring systems is additive. The additivity indicates that inter-ring interactions which effect the central bond length are absent and confirms the common electronic origin of bond contraction in these systems, viz. enhanced s-character in the exocyclic bonds of strained rings.

Position and Feed-Rate Control for Contouring Numerical-Control Systems

Numerical control (NC) for contouring operations requires precise control of position and feed rate for approximating the contour by linear moves of the cutter. A control scheme, for generating linear moves with desired slopes for the cutter, is described. This scheme provides for nine successive linear moves, and may be either expanded or implemented in succession, for approximating a contour.

Local approximability of max-min and min-max linear programs

In a max-min LP, the objective is to maximise ω subject to Ax ≤ 1, Cx ≥ ω1, and x ≥ 0. In a min-max LP, the objective is to minimise ρ subject to Ax ≤ ρ1, Cx ≥ 1, and x ≥ 0. The matrices A and C are nonnegative and sparse: each row ai of A has at most ΔI positive elements, and each row ck of C has at most ΔK positive elements. We study the approximability of max-min LPs and min-max LPs in a distributed setting; in particular, we focus on local algorithms (constant-time distributed algorithms). We show that for any ΔI ≥ 2, ΔK ≥ 2, and ε > 0 there exists a local algorithm that achieves the approximation ratio ΔI (1 − 1/ΔK) + ε. We also show that this result is the best possible: no local algorithm can achieve the approximation ratio ΔI (1 − 1/ΔK) for any ΔI ≥ 2 and ΔK ≥ 2.

A homotopy approach for stabilizing single-input systems with control structure constraints

A linear state feedback gain vector used in the control of a single input dynamical system may be constrained because of the way feedback is realized. Some examples of feedback realizations which impose constraints on the gain vector are: static output feedback, constant gain feedback for several operating points of a system, and two-controller feedback. We consider a general class of problems of stabilization of single input dynamical systems with such structural constraints and give a numerical method to solve them. Each of these problems is cast into a problem of solving a system of equalities and inequalities. In this formulation, the coefficients of the quadratic and linear factors of the closed-loop characteristic polynomial are the variables. To solve the system of equalities and inequalities, a continuous realization of the gradient projection method and a barrier method are used under the homotopy framework. Our method is illustrated with an example for each class of control structure constraint.

A High Pressure Study of the Phase Diagram and the Critical Exponent β of Binary Liquid Systems

The pressure dependence of critical parameters xc, Tc, and β have been analysed in four systems namely cyclohexane + acetic anhydride, n-heptane + acetic anhydride, methanol + n-heptane, and carbon disulphide + acetonitrile. The separation temperature was found to increase linearly with pressure the value of dTc/dP being 28 mK, 11 mK, 22 mK, and 25 mK respectively. These are in fair agreement with earlier measurements available for two systems. For the methanol + n-heptane system dTc/dP is apparently not consistent with the value predicted from the specific heat and thermal expansion data.Die Druckabhängigkeit der kritischen Parameter xc, Tc und β ist in den vier Systemen Cyclohexan + Essigsäureanhydrid, n-Heptan + Essigsäureanhydrid, Methanol + n-Heptan und Schwefelkohlenstoff + Acetonitril analysiert worden. Es wurde gefunden, daß die kritische Temperatur linear mit dem Druck ansteigt. Die Werte für dTc/dP betragen 28 mK, 11 mK, 22 mK und 25 mK. Sie sind in guter überein-stimmung mit früheren Messungen an zweien dieser Systeme. Für Methanol + n-Heptan stimmt der Wert für dT/dP offensichtlich nicht mit Werten, die mit Hilfe von Daten für die spezifische Wärme und die thermische Ausdehnung vorhergesagt wurden, überein.

A structural principle for a class of adaptive systems

A feature common to many adaptive systems for identification and control is the adjustment.of gain parameters in a manner ensuring the stability of the overall system. This paper puts forward a principle which assures such a result for arbitrary systems which are linear and time invariant except for the adjustable parameters. The principle only demands that a transfer function be positive real. This transfer function dependent on the structure of the system with respect to the parameters. Several examples from adaptive identification, control and observer schemes are given as illustrations of the conceptual simplification provided by the structural principle.

Exact traveling- wave solution for model geophysical systems

Exact traveling-wave solutions of time-dependent nonlinear inhomogeneous PDEs, describing several model systems in geophysical fluid dynamics, are found. The reduced nonlinear ODEs are treated as systems of linear algebraic equations in the derivatives. A variety of solutions are found, depending on the rank of the algebraic systems. The geophysical systems include acoustic gravity waves, inertial waves, and Rossby waves. The solutions describe waves which are, in general, either periodic or monoclinic. The present approach is compared with the earlier one due to Grundland (1974) for finding exact solutions of inhomogeneous systems of nonlinear PDEs.

Relationship Between The Impedance Matrix And The Transfer Matrix With Specific Reference To Symmetrical, Reciprocal And Conservative Systems

Impedance matrix and transfer matrix methods are often used in the analysis of linear dynamical systems. In this paper, general relationships between these matrices are derived. The properties of the impedance matrix and the transfer matrix of symmetrical systems, reciprocal systems and conservative systems are investigated. In the process, the following observations are made: (a) symmetrical systems are not a subset of reciprocal systems, as is often misunderstood; (b) the cascading of reciprocal systems again results in a reciprocal system, whereas cascading of symmetrical systems does not necessarily result in a symmetrical system; (c) the determinant of the transfer matrix, being ±1, is a property of both symmetrical systems and reciprocal systems, but this condition, however, is not sufficient to establish either the reciprocity or the symmetry of the system; (d) the impedance matrix of a conservative system is skew-Hermitian.

BER Analysis of Weighted Interference Cancellation in Multicarrier DS-CDMA Systems

In this paper, we present the design and bit error performance analysis of weighted linear parallel interference cancellers (LPIC) for multicarrier (MC) DS-CDMA systems. We propose an LPIC scheme where we estimate (and cancel) the multiple access interference (MAI) based on the soft outputs on individual subcarriers, and the interference cancelled outputs on different subcarriers are combined to form the final decision statistic. We scale the MAI estimate on individual subcarriers by a weight before cancellation; these weights are so chosen to maximize the signal-to-interference ratios at the individual subcarrier outputs. For this weighted LPIC scheme, using an approach involving the characteristic function of the decision variable, we derive exact bit error rate (BER) expressions for different cancellation stages. Using the same approach, we also derive exact BER expressions for the matched filter (MF) and decorrelating detectors for the considered MC DS-CDMA system. We show that the proposed weighted LPIC scheme performs better than the MF detector and the conventional LPIC (where the weights are taken to be unity), and close to the decorrelating detector.

Points-to Analysis as a System of Linear Equations

We propose a novel formulation of the points-to analysis as a system of linear equations. With this, the efficiency of the points-to analysis can be significantly improved by leveraging the advances in solution procedures for solving the systems of linear equations. However, such a formulation is non-trivial and becomes challenging due to various facts, namely, multiple pointer indirections, address-of operators and multiple assignments to the same variable. Further, the problem is exacerbated by the need to keep the transformed equations linear. Despite this, we successfully model all the pointer operations. We propose a novel inclusion-based context-sensitive points-to analysis algorithm based on prime factorization, which can model all the pointer operations. Experimental evaluation on SPEC 2000 benchmarks and two large open source programs reveals that our approach is competitive to the state-of-the-art algorithms. With an average memory requirement of mere 21MB, our context-sensitive points-to analysis algorithm analyzes each benchmark in 55 seconds on an average.