Stability of linear time-invariant discrete systems

The Fundamental stability theorem giving the input-output properties of linear time-invariant discrete systems is extended to include multiple poles on or outside the unit circle and to include properties of the error coefficients. The engineering significance of some of the assumptions is discussed.     

Testing the controllability of linear time-invariant systems

A method for studying the controllability of a linear time-invariant system by considering the controllability of a smaller subsystem is proposed. The method is most effective when the system under study has a large number of inputs and states.     

Disturbance localisation in linear time-invariant multivariable systems

A simple algebraic approach is used to derive necessary and sufficient conditions for the existence of a state feedback matrix to localise disturbances and which some of the closed-loop-system eigenvectors must satisfy for disturbance localisation. This latter result provides valuable insight as to how the state feedback matrix may be synthesised.     

Dyadic modal control of multi-input time-invariant linear systems

In the letter, a closed-form formula is presented for the feedback gains required to assign arbitrary eigenvalues to the closed-loop system matrix of a class of multi-input systems.     

Steady-state quantum analysis of linear systems

A rigorous basis for the quantum analysis of the steady state of linear distributed systems is established. The analysis of a distributed system of finite length requires, for self-consistency, that excitations be stated at the boundaries of the system even in the absence of externally applied excitations. The commutators of the amplitudes at the boundaries are stated and a useful analogy with thermal noise of classical systems is established. The use of these boundary conditions enables one to formulate the theory of the steady state for distributed quantum systems. When the system under consideration is coupled to a dissipation mechanism, operator-noise sources have to be assigned to the dissipative elements. The commutation relations that must be obeyed by these noise sources are derived. This formalism enables one to analyze the steady-state operation of an attenuator and of a maser amplifier. Finally, properties of multiterminal-pair networks are discussed using the steady-state quantum approach.     

On compensator design for linear time-invariant dual-inputsingle-output systems

This paper presents a new method for the design of compensators for linear time-invariant dual-input/single-output (DISO) systems in continuous time or discrete time. The new method reduces the problem to two single-input/single-output (SISO) design problems, which are well suited to frequency-response design techniques. The first part of the method is the design of a stabilizing compensator for an auxiliary feedback system. The auxiliary compensator parameterizes the two output blocks of the single-input/dual-output compensator such that the zeros of the parallel system formed by cascade of the compensator with the plant are stable. The auxiliary compensator also determines the relative contribution to the output of the two parallel subsystems of the DISO system. The second SISO compensator design is used to ensure that the feedback system is stable and that performance and robustness specifications are achieved. This paper includes a discrete-time-design example for a dual-stage actuator system for a disk drive including implementation results. Straightforward extensions for multi-input/single-output systems are discussed     

Calculation of piecewise-constant control strategies for linear time-invariant systems

A method is derived for computing piecewise-constant control strategies to transfer the state of a controllable linear system described by the vector-matrix equation dx/dt = Ax+Bu from the initial state x(0) to a specified state x(tn) in a specified time tn.     

Modal control of multivariable time-invariant linear systems by output feedback

It is shown that, for a certain class of time-invariant linear systems, modal control can be effected by using output rather than state feedback.     

Normality conditions for the time-optimal control of time-invariant linear systems

Two conditions are presented concerning the normality of the time-optimal control of a class of time-invariant systems with bounded control input vectors. The theoretical and practical significance of these results is discussed, and the results are illustrated by numerical examples.     

Method of modelling linear time-invariant distributed-parameter systems by pseudorandom binary sequences

A method of deriving lumped-parameter difference equation models of linear time-invariant distributed-parameter systems using pseudorandom binary sequences (p.r.b.s.) is described. Results from the application of the method to a diffusion process are presented.     

Dyadic modal control of multi-input time-invariant linear systems incorporating integral feedback

In the letter, the possibility of applying dyadic modal control to multi-input time-invariant linear systems incorporating integral-feedback action is investigated. In those cases for which such application is possible, simple closed-form formulas are obtained for the feedback-loop gains of the appropriate dyadic modal controller.     

A note on identification of linear time-invariant systems using exponential curve fitting

A simple method of system identification for linear time-invariant systems based on exponential curve fitting of impulse response data is presented. The simplicity of the method which does not require determination of initial conditions is the result of choosing appropriate discrete-time state-variable models.     

Algebraic relations between system response and system parameters for linear time-invariant systems

By means of a rational-fraction approximation to the delay function, and through use of a generalised technique for evaluating convolution integrals, it is possible to approximately evaluate the inverse Laplace transform. The time-domain response is approximated by a ratio of polynomials in t, with coefficients which are algebraic functions of the system parameters.     

Synthesis of asymptotically stable linear time-invariant closed-loop systems incorporating multivariable 3-term controllers

An inverse Lyapunov technique is presented for the design of asymptotically stable linear time-invariant closed-loop systems incorporating multivariable 3-term controllers.     

Comment: Synthesis of asymptotically stable linear time-invariant closed-loop systems incorporating multivariable 3-term controllers

The letter contains some elementary observations on a letter in which an inverse Lyapunov technique was propounded as a means for obtaining `gain? matrices in such a manner that a linear 3-term controlled closed-loop system was rendered asymptotically stable. While that letter is rigorously correct in most respects, some simple properties of the constituent matrices were overlooked and others were masked by the adoption of the Lyapunov method.     

Identification of linear time-invariant system using feedback gain

Feedback property and exponential curve fitting are used to identify the parameters of transfer function. It is assumed that all state variables are inaccessible for measurement.     

Acoustic FMRI noise: linear time-invariant system model

Functional magnetic resonance imaging (fMRI) enables sites of brain activation to be localized in human subjects. For auditory system studies, however, the acoustic noise generated by the scanner tends to interfere with the assessments of this activation. Understanding and modeling fMRI acoustic noise is a useful step to its reduction. To study acoustic noise, the MR scanner is modeled as a linear electroacoustical system generating sound pressure signals proportional to the time derivative of the input gradient currents. The transfer function of one MR scanner is determined for two different input specifications: 1) by using the gradient waveform calculated by the scanner software and 2) by using a recording of the gradient current. Up to 4 kHz, the first method is shown as reliable as the second one, and its use is encouraged when direct measurements of gradient currents are not possible. Additionally, the linear order and average damping properties of the gradient coil system are determined by impulse response analysis. Since fMRI is often based on echo planar imaging (EPI) sequences, a useful validation of the transfer function prediction ability can be obtained by calculating the acoustic output for the EPI sequence. We found a predicted sound pressure level (SPL) for the EPI sequence of 104 dB SPL compared to a measured value of 102 dB SPL. As yet, the predicted EPI pressure waveform shows similarity as well as some differences with the directly measured EPI pressure waveform.