Explicit formulae for completions of linear time varying singular systems of differential equations

Completions of linear time varying singular systems of the formE(t)x(t)+F(t)x(t)=f(t) are explicitly computed using recent results on rational matrix functions. The algorithm and the theory behind it are carefully described. Computational issues are discussed.Research supported in part by the U.S. Army Research Office under DAAL03-89-D-0003, and the National Science Foundation under ECS-9012909.     

Stability of impulsive linear differential equations with time delay

In this paper, we consider the stability of impulsive linear differential equations with time delay. By using Lyapunov functions and analysis technique, we get some results for the stability of impulsive linear differential equations with time delay. An example is also discussed to illustrate the efficiency of the obtained results.     

Stability for composite singular systems of differential equations with a delay

In this paper, we gave an exponential estimate for the solutions of singular systems of differential equations with a delay and establish a comparison inequality for the systems. Based on this we estabish the criteria for asymptotic stability for the composite singular systems.     

Transfer functions attached to linear systems with time varying parameters

To obtain transfer functions attached to linear time varying (Ltv) systems, a new method for getting the poles and residia of linear time invariant (Lti) continuous or discrete systems is proposed. The explored method is superior to others known, because it can be extended to systems with time varying parameters. With the poles and residia so obtained, the transfer function attached to the ltv systems, both continuous and discrete, results easily.     

A survey of linear singular systems

This paper is a brief historical review of linear singular systems, followed by a survey of results on their solution and properties. The frequency domain and time domain approaches are discussed together to sketch an overall picture of the current status of the theory.     

Turbo space-time codes with time varying linear transformations

Turbo space-time codes with symbols precoded by randomly chosen unitary time variant linear transformations (TVLT) are investigated in this paper. It is shown that turbo codes with TVLT achieve full diversity gain and do not require exhaustive tests of the rank criterion. We prove that the coding gain performance of turbo space-time codes with TVLT improves with the Hamming distance between codewords (number of different columns). As an additional benefit of the application of TVLT, with the removal of the constant modulation condition, we prove that throughput rates achieved by these codes are significantly higher than those for conventional space-time codes. Numerical results are provided to demonstrate diversity gains, coding gains and rates of turbo space-time codes with TVLT     

Random-access systems with a time varying channel

A random multiple-access system which employs a collision resolution algorithm for accessing a common time-varying channel is considered. The channel is assumed to be in one of two states. In each state, the channel is characterized by a general discrete memoryless channel and the transitions between the two states are assumed to be Markovian. A set of sufficient conditions for the ergodicity (stability) of the system is established. As an example, the case when the Capetanakis tree algorithm operates with a time-varying noisy channel is examined. The stability of this system is analyzed, and the throughput is evaluated     

Stability of constant coefficient linear singular systems with delay

In this paper, the general class of singular systems with delay and linear constant coefficient singular systems with delay are discussed. First, several definitions of stability are presented for singular systems with delay, and general sufficient stability conditions and instability conditions are obtained. Second, stability and instability are analyzed for linear constant coefficient singular systems with delay.This project was supported by the Guangdong Provincial Natural Science Foundation of China, No. 990584.     

One canonical form for higher-index linear time-varying singular systems

One form of the singular systemAx+Bx=f is considered. The analytic solution, perturbation, and numerical solution of this form are examined. A class of systems which may be transformed into this form without altering these properties is characterized.Research sponsored by Air Force Office of Scientific Research, Air Force Systems Command, under Grant No. AFOSR-81-0052A. The United States Government is authorized to reproduce and distribute reprints for governmental purposes not with-standing any copyright notation here on.     

Initial conditions and initialization of linear fractional differential equations

Mastery of the initial conditions of fractional order systems remains an open problem, in spite of a great number of contributions. This paper proposes a solution dedicated to linear fractional differential equations (FDEs), which is based on an equivalence principle between the original system and an exactly equivalent infinite dimensional ordinary differential equation (ODE). This equivalence principle is derived from the fractional integration operator concept and the frequency distributed state space model of this operator. Thanks to this principle, the FDE initial conditions problem is converted into a conventional ODE initialization problem, however with an infinite dimensional state vector. Practical FDE initialization is performed using an observer based technique applied to the equivalent ODE; a numerical example demonstrates the efficiency of this approach.     

Characteristic equations of optimal linear multivariable control systems

A simple derivation of the frequency-domain characteristic equation of the optimal linear multivariable control system is given. The equation is obtained from Pontryagin's maximum principle and is compared with alternative expressions given in the literature.     

Control of linear systems with time delay

Luenberger's procedure for the design of controllers of linear systems with inaccessible state vectors is extended to deal with time-delay systems.     

A nullstellensatz for linear partial differential equations with polynomial coefficients

Multidimensional Systems and Signal Processing - In this paper an equation means a homogeneous linear partial differential equation in n unknown functions of m variables which has real or complex...     

Solution of dense systems of linear equations arising fromintegral-equation formulations

This paper discusses the efficient solution of dense systems of linear equations, arising from integral-equation formulations. Several preconditioners, in connection with Krylov iterative solvers, are examined, and compared with LU factorization. Results are shown, demonstrating practical aspects and issues we have encountered in implementing iterative solvers, on both parallel and sequential computers, for a magnetostatic volume-integral formulation     

Instantaneous characterization of time varying nonlinear systems[neurophysiological responses]

A nonlinear system may be characterized by an orthogonal functional power series (FPS) computed from cross correlations between input and output variables. "Is the response changing over the course of the experiment?" is a fundamental question encountered in the analysis of both FPS and evoked potentials (EP's). Regression on closed-form functions of time produces a time-varying FPS or EP. Evaluation of these functions at a specified time point produces a system characterization for that instant.     

Efficient algorithms for solving modified matrix equations of linear systems

Multiparameter change in linear algebraic systems is investigated systematically by a parameter matrix decomposition of the modified system interaction matrix. Transformation of the corresponding modified response matrix to a parameter representation considerably reduces the computation of system response. Three highly efficient response change algorithms are formulated and critically compared.     

Identification of models for discrete linear systems with variable,slowly varying parameters

The article suggests a solution to the problem of identification of models for discrete linear systems with variable, slowly varying parameters. It is established that the solution can be obtained via minimization of empirical loss functions with equality restrictions defined on a sequence of local intervals. It is shown that the identification is provided with the help of a sequence of functional polynomials satisfying the required conditions of smooth joining. In particular, periodically varying parameters of discrete systems associated with a digital resonator are identified with the use of polynomials of exponential functions.     

Analysis of free processes in time varying circuit by means of generalized characteristic equations method

Developing methods of analysis of free processes in time varying circuit is important both for time varying and nonlinear radio circuits. The principle of linear connection brings together processes in time varying and nonlinear circuits. It is of special interest to extend the existing methods developed for radio circuits with stable parameters to time varying circuits. This article is devoted to one of such methods-the method of characteristic equations for differential equations with fixed factors.     

Synthesis of linear optimum distributed parameter systems with time delays

A variational calculus approach is used to study quadratic optimization of linear time-delayed distributed parameter systems with distributed and boundary control function. The canonical equations are derived for the necessary condition of optimality. Then the Riccati equations are obtained and their computational solution is discussed.