L2-stability of nonstationary feedback systems: Frequency-domain criteria

A frequency-domain positivity condition is derived for linear time-varying operators in2and is used to develop2stability criteria for linear and nonlinear feedback systems. These criteria permit the use of a very general class of operators in2with nonstationary kernels, as multipliers. More specific results are obtained by using a first-order differential operator with a time-varying coefficient as multiplier. Finally, by employing periodic multipliers, improved stability criteria are derived for the nonlinear damped Mathieu equation with a forcing function.

Improved Conditions For L2-Stability Of Nonstationary Feedback-Systems

Concerning the L2-stability of feedback systems containing a linear time-varying operator, some of the stringent restrictions imposed on the multiplier as well as the linear part of the system, in the criteria presented earlier, are relaxed.

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.

On the L2 stability of linear multidimensional time varying systems

This paper analyzes the L2 stability of solutions of systems with time-varying coefficients of the form [A + C(t)]x′ = [B + D(t)]x + u, where A, B, C, D are matrices. Following proof of a lemma, the main result is derived, according to which the system is L2 stable if the eigenvalues of the coefficient matrices are related in a simple way. A corollary of the theorem dealing with small periodic perturbations of constant coefficient systems is then proved. The paper concludes with two illustrative examples, both of which deal with the attitude dynamics of a rigid, axisymmetric, spinning satellite in an eccentric orbit, subject to gravity gradient torques.

Average variation L2-stability criteria for time-varying feedback systems-A unified approach

The problem of developing L2-stability criteria for feedback systems with a single time-varying gain, which impose average variation constraints on the gain is treated. A unified approach is presented which facilitates the development of such average variation criteria for both linear and nonlinear systems. The stability criteria derived here are shown to be more general than the existing results.

Syntheses and structural investigation of some alkali metal ion-mediated (LVO2-)-O-V (L2- = tridentate ONO ligands) species: DNA binding, photoinduced DNA cleavage and cytotoxic activities

Eight alkali metal ion-mediated dioxidovanadium(V), {(VO2L1-6)-O-V} A(H2O)n]proportional to, complexes for A = Li+, Na+, K+ and Cs+, containing tridentate aroylhydrazonate ligands coordinating via ONO donor atoms, are described. All the synthesised ligands and the metal complexes were successfully characterised by elemental analysis, IR, UV-Vis and NMR spectroscopy. X-ray crystallographic investigation of 3, 5-7 shows the presence of distorted NO4 coordination geometries for LVO2- in each case, and varying mu-oxido and/ or mu-aqua bridging with interesting variations correlated with the size of the alkali metal ions: with small Li+, no bridging-O is found but four ion aggregates are found with Na+, chains for K+ and finally, layers for Cs+. Two (5) or three-dimensional (3, 6 and 7) architectures are consolidated by hydrogen bonding. The dioxidovanadium(V) complexes were found to exhibit DNA binding activity due to their interaction with CT-DNA by the groove binding mode, with binding constants ranging from 10(3) to 10(4) M-1. Complexes 1-8 were also tested for DNA nuclease activity against pUC19 plasmid DNA which showed that 6 and 7 had the best DNA binding and photonuclease activity; these results support their good protein binding and cleavage activity with binding constants ranging from 104 to 105 M-1. Finally, the in vitro antiproliferative activity of all complexes was assayed against the HeLa cell line. Some of the complexes (2, 5, 6 and 7) show considerable activity compared to commonly used chemotherapeutic drugs. The variation in cytotoxicity of the complexes is influenced by the various functional groups attached to the aroylhydrazone derivative.

x-ray studies on crystalline complexes involving amino-acids and peptides .10. head-to-tail sequences in the crystal-structure of l-lysine acetate

l-Lysine acetate crystallises in the monoclinic space group P21 with a = 5.411 (1), b = 7.562(1), c= l2.635(2) Å and β = 91.7(1). The crystal structure was solved by direct methods and refined to an R value of 0.049 using the full matrix least squares method. The conformation and the aggregation of lysine molecules in the structure are similar to those found in the crystal structure of l-lysine l-aspartate. A conspicuous similarity between the crystal structures of l-arginine acetate and l-lysine acetate is that in both cases the strongly basic side chain, although having the largest pK value, interacts with the weakly acidic acetate group leaving the α-amino and the α-carboxylate groups to take part in head-to-tail sequences. These structures thus indicate that electrostatic effects are strongly modulated by other factors so as to give rise to head-to-tail sequences which have earlier been shown to be an almost universal feature of amino acid aggregation in the solid state.

Focused Prefetching: Performance Oriented Prefetching Based On Commit Stalls

Loads that miss in L1 or L2 caches and waiting for their data at the head of the ROB cause significant slow down in the form of commit stalls. We identify that most of these commit stalls are caused by a small set of loads, referred to as LIMCOS (Loads Incurring Majority of COmmit Stalls). We propose simple history-based classifiers that track commit stalls suffered by loads to help us identify this small set of loads. We study an application of these classifiers to prefetching. The classifiers are used to train the prefetcher to focus on the misses suffered by LIMCOS. This, referred to as focused prefetching, results in a 9.8% gain in IPC over naive GHB based delta correlation prefetcher along with a 20.3% reduction in memory traffic for a set of 17 memory-intensive SPEC2000 benchmarks. Another important impact of focused prefetching is a 61% improvement in the accuracy of prefetches. We demonstrate that the proposed classification criterion performs better than other existing criteria like criticality and delinquent loads. Also we show that the criterion of focusing on commit stalls is robust enough across cache levels and can be applied to any prefetcher without any modifications to the prefetcher.

Time-domain criteria for theL_{2}-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.

L_{2}- stability of a class of nonstationary feedback systems with dynamical nonlinear subsystems

A class of feedback systems, consisting of dynamical non-linear subsystems which arise in many diverse control applications, is analyzed for L2-stability. It is shown that, although a transformation of these systems to the familiar Lur'e configuration does not seem to be possible, a one-to-one correspondence may be effected between the stability properties of these and the Lur'e systems. Interesting stability criteria are developed by exploiting this characteristic.

On the positivity and stability of non-stationary systems

The positivity of operators in Hilbert spaces is an important concept finding wide application in various branches of Mathematical System Theory. A frequency- domain condition that ensures the positivity of time-varying operators in L2 with a state-space description, is derived in this paper by using certain newly developed inequalities concerning the input-state relation of such operators. As an interesting application of these results, an L2 stability criterion for time-varying feedback systems consisting of a finite-sector non-linearity is also developed.

Application of optimization methods to vibration control of stretched strings

In this paper, non-linear programming techniques are applied to the problem of controlling the vibration pattern of a stretched string. First, the problem of finding the magnitudes of two control forces applied at two points l1 and l2 on the string to reduce the energy of vibration over the interval (l1, l2) relative to the energy outside the interval (l1, l2) is considered. For this problem the relative merits of various methods of non-linear programming are compared. The more complicated problem of finding the positions and magnitudes of two control forces to obtain the desired energy pattern is then solved by using the slack unconstrained minimization technique with the Fletcher-Powell search. In the discussion of the results it is shown that the position of the control force is very important in controlling the energy pattern of the string.