A survey of methods for generating Liapunov functions.
Liapunov functions generating methods applicable to nonlinear and linear autonomous systems
LIAPUNOV FUNCTION↗
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Results for “linear systems”
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Linear regulator design for stochastic systems by a multiple time scales method
A hierarchically-structured, suboptimal controller for a linear stochastic system composed of fast and slow subsystems is considered. The controller is optimal in the limit as the separation of time scales of the subsystems becomes infinite. The methodology is illustrated by design of a controller to suppress the phugoid and short period modes of the longitudinal dynamics of the F-8 aircraft.
Teneketzis, D.↗
Quadrature, Interpolation and Observability
Methods of interpolation and quadrature have been used for over 300 years. Improvements in the techniques have been made by many, most notably by Gauss, whose technique applied to polynomials is referred to as Gaussian Quadrature. Stieltjes extended Gauss's method to certain non-polynomial functions as early as 1884. Conditions that guarantee the existence of quadrature formulas for certain collections of functions were studied by Tchebycheff, and his work was extended by others. Today, a class of functions which satisfies these conditions is called a Tchebycheff System. This thesis contains the definition of a Tchebycheff System, along with the theorems, proofs, and definitions necessary to guarantee the existence of quadrature formulas for such systems. Solutions of discretely observable linear control systems are of particular interest, and observability with respect to a given output function is defined. The output function is written as a linear combination of a collection of orthonormal functions. Orthonormal functions are defined, and their properties are discussed. The technique for evaluating the coefficients in the output function involves evaluating the definite integral of functions which can be shown to form a Tchebycheff system. Therefore, quadrature formulas for these integrals exist, and in many cases are known. The technique given is useful in cases where the method of direct calculation is unstable. The condition number of a matrix is defined and shown to be an indication of the the degree to which perturbations in data affect the accuracy of the solution. In special cases, the number of data points required for direct calculation is the same as the number required by the method presented in this thesis. But the method is shown to require more data points in other cases. A lower bound for the number of data points required is given.
Hodges, Lucille McDaniel↗
Strain accumulation in quasicrystalline solids
The relaxation of two-dimensional quasicrystalline elastic networks when their constituent bonds are perturbed homogeneously is studied. Whereas ideal, quasi-periodic networks are stable against such perturbations, significant accumulations of strain in a class of disordered networks generated by a growth process are found. The grown networks are characterized by root mean square phason fluctuations which grow linearly with system size. The strain accumulation observed in these networks also grows linearly with system size. Finally, dependence of strain accumulation on cooling rate is found.
Nori, Franco↗
Nordheim-Gorter like behavior and one carrier conduction in a quasi-one-dimensional system
A linear correlation has been observed between the thermopower and the conductivity in the high-temperature state (T greater than 220 K) of the TTF halide and pseudohalide salts. It is suggested that this correlation indicates conduction by a single type of carrier under two types of scattering and represents the first reported extension of the Nordheim-Gorter behavior to any quasi-one-dimensional conductor.
Datta, T.↗
Dynamic Range Enhancement of High-Speed Electrical Signal Data via Non-Linear Compression
Systems and methods for high-speed compression of dynamic electrical signal waveforms to extend the measuring capabilities of conventional measuring devices such as oscilloscopes and high-speed data acquisition systems are discussed. Transfer function components and algorithmic transfer functions can be used to accurately measure signals that are within the frequency bandwidth but beyond the voltage range and voltage resolution capabilities of the measuring device.
Laun, Matthew C.↗
System and Method for Generating a Frequency Modulated Linear Laser Waveform
A system for generating a frequency modulated linear laser waveform includes a single frequency laser generator to produce a laser output signal. An electro-optical modulator modulates the frequency of the laser output signal to define a linear triangular waveform. An optical circulator passes the linear triangular waveform to a band-pass optical filter to filter out harmonic frequencies created in the waveform during modulation of the laser output signal, to define a pure filtered modulated waveform having a very narrow bandwidth. The optical circulator receives the pure filtered modulated laser waveform and transmits the modulated laser waveform to a target.
Pierrottet, Diego F.↗
System and Method for Generating a Frequency Modulated Linear Laser Waveform
A system for generating a frequency modulated linear laser waveform includes a single frequency laser generator to produce a laser output signal. An electro-optical modulator modulates the frequency of the laser output signal to define a linear triangular waveform. An optical circulator passes the linear triangular waveform to a band-pass optical filter to filter out harmonic frequencies created in the waveform during modulation of the laser output signal, to define a pure filtered modulated waveform having a very narrow bandwidth. The optical circulator receives the pure filtered modulated laser waveform and transmits the modulated laser waveform to a target.
Pierrottet, Diego F.↗
Extended observability of linear time-invariant systems under recurrent loss of output data
Recurrent loss of sensor data in integrated control systems of an advanced aircraft may occur under different operating conditions that include detected frame errors and queue saturation in computer networks, and bad data suppression in signal processing. This paper presents an extension of the concept of observability based on a set of randomly selected nonconsecutive outputs in finite-dimensional, linear, time-invariant systems. Conditions for testing extended observability have been established.
Luck, Rogelio↗
Linear regulator design for stochastic systems by a multiple time scales method
This paper develops a hierarchically-structured, suboptimal controller for a linear stochastic system composed of fast and slow subsystems. It is proved that the controller is optimal in the limit as the separation of time scales of the subsystems becomes infinite. The methodology is illustrated by design of a controller to suppress the phugoid and short period modes of the longitudinal dynamics of the F-8 aircraft.
Teneketzis, D.↗
Minimum principle for a nonequilibrium stochastic system.
Minimum principle characterizing steady state of linear stochastic system found by using urn model
STOCHASTIC PROCESS↗
Optimal inputs for system identification
Identification criteria are presented for linear dynamic systems with and without process noise. With process noise, the state equations are replaced by the Kalman filter equations. If the identification performance index is expanded in a Taylor's series with respect to the parameters to be identified, then maximizing the weighting factor of the quadratic term with respect to the inputs will insure that an identification algorithm will converge more rapidly and to a more accurate result than with nonoptimal inputs. The expectation of this weighting factor is the Fisher information matrix, and its inverse is a lower bound for the covariance of the parameters. Direct and indirect methods of calculating the information matrix are presented for systems with and without process noise.
Reid, D. B.↗
Development of deployable structures for large space platform systems. Volume 1: Executive summary
Candidate deployable linear platform system concepts suitable for development to technology readiness by 1986 are reviewed. The systems concepts were based on trades of alternate deployable/retractable structure concepts, integration of utilities, and interface approaches for docking and assembly of payloads and subsystems. The deployable volume studies involved generation of concepts for deployable volumes which could be used as unpressurized or pressurized hangars, habitats and interconnecting tunnels. Concept generation emphasized using flexible materials and deployable truss structure technology.
Cox, R. L.↗
The algebraic criteria for the stability of control systems
This paper critically examines the standard algebraic criteria for the stability of linear control systems and their proofs, reveals important previously unnoticed connections, and presents new representations. Algebraic stability criteria have also acquired significance for stability studies of non-linear differential equation systems by the Krylov-Bogoljubov-Magnus Method, and allow realization conditions to be determined for classes of broken rational functions as frequency characteristics of electrical network.
Cremer, H.↗
Linear regulator design for stochastic systems by a multiple time-scales method
This short paper develops a hierarchically structured, suboptimal controller for a linear stochastic system composed of fast and slow subsystems. It is proved that the controller is optimal in the limit as the separation of time scales of the subsystems becomes infinite. The methodology is illustrated by design of a controller to suppress the phugoid and short-period modes of the longitudinal dynamics of the F-8 aircraft.
Teneketzis, D.↗
Synthesis procedure for linear time-varying feedback systems with large parameter ignorance
The development of synthesis procedures for linear time-varying feedback systems is considered. It is assumed that the plant can be described by linear differential equations with time-varying coefficients; however, ignorance is associated with the plant in that only the range of the time-variations are known instead of exact functional relationships. As a result of this plant ignorance the use of time-varying compensation is ineffective so that only time-invariant compensation is employed. In addition, there is a noise source at the plant output which feeds noise through the feedback elements to the plant input. Because of this noise source the gain of the feedback elements must be as small as possible. No attempt is made to develop a stability criterion for time-varying systems in this work.
Mcdonald, T. E., Jr.↗
A controllability theory for nonlinear systems
Liapunov approach to nonlinear dynamic systems controllability, deriving conditions for linear dynamic systems
Gershwin, S. B.↗
Morphological instability in a float zone
This paper examines the morphological instability of the freezing interface of the float zone in a crystal sheet for which the height of the liquid zone L = Lf + Lm (where Lf and Lm are the planar positions of the solidifying and melting interfaces) is smaller than the width and the thickness of the sheet. The Lf and Lm positions are calculated, and basic state concentration profiles are determined for a planar interfacial system. A linear stability analysis of this system is performed showing that the growth rate of disturbances is a modified version of the growth rate for a directional solidification system. It was found that shorter melt zone configurations are less susceptible to long wavelength morphological instability, indicating that, to suppress morphological instability in a float zone system, it is necessary to decrease the liquid zone height.
Humphreys, Laura B.↗