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Callier, F. M.

Publications and source records attributed to Callier, F. M..

11 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

Necessary and sufficient conditions for the complete controllability and observability of systems in series using the coprime factorization of a rational matrix

The series connection of two linear time-invariant systems that have minimal state space system descriptions is considered. From these descriptions, strict-system-equivalent polynomial matrix system descriptions in the manner of Rosenbrock are derived. They are based on the factorization of the transfer matrix of the subsystems as a ratio of two right or left coprime polynomial matrices. They give rise to a simple polynomial matrix system description of the tandem connection. Theorem 1 states that for the complete controllability and observability of the state space system description of the series connection, it is necessary and sufficient that certain 'denominator' and 'numerator' groups are coprime. Consequences for feedback systems are drawn in Corollary 1. The role of pole-zero cancellations is explained by Lemma 3 and Corollaires 2 and 3.

Callier, F. M.↗
NASA NTRS1974

L/superscript-p/ stability /p ranging from 1 to infinity/ of multivariable non-linear time-varying feedback systems that are open-loop unstable

The loop transformation technique (Sandberg, 1965; Zames, 1966, Willems, 1971), and the fixed point theorem (Schwartz, 1970) are used to derive the L(superscript-p) stability for a class of multivariable nonlinear time-varying feedback systems which are open-loop unstable. The application of the fixed point theorem in L(superscript-p) shows that the nonlinear feedback system has one and only one solution for any pair of inputs in L(superscript-p), that the solutions are continuously dependent on the inputs, and that the closed loop system is L(superscript-p)-stable for any p ranging from 1 to infinity.

Callier, F. M.↗
NASA NTRS1973

Lp-stability (1 less than or equal to p less than or equal to infinity) of multivariable nonlinear time-varying feedback systems that are open-loop unstable

A class of multivariable, nonlinear time-varying feedback systems with an unstable convolution subsystem as feedforward and a time-varying nonlinear gain as feedback was considered. The impulse response of the convolution subsystem is the sum of a finite number of increasing exponentials multiplied by nonnegative powers of the time t, a term that is absolutely integrable and an infinite series of delayed impulses. The main result is a theorem. It essentially states that if the unstable convolution subsystem can be stabilized by a constant feedback gain F and if incremental gain of the difference between the nonlinear gain function and F is sufficiently small, then the nonlinear system is L(p)-stable for any p between one and infinity. Furthermore, the solutions of the nonlinear system depend continuously on the inputs in any L(p)-norm. The fixed point theorem is crucial in deriving the above theorem.

Callier, F. M.↗
NASA NTRS1972

A graphical test for checking the stability of a linear time-invariant feedback system.

A continuous-time scalar linear time-invariant feedback system is considered for the purpose of checking Willems' (1969, 1970) graphical test for a scalar linear time-invariant feedback system with constant feedback. Heavy reliance is placed on the theory of almost periodic functions. Following definition of the problem and layout of notation, attention is given to solution of the problem, considering only the almost periodic part of the open-loop transfer function.

Callier, F. M.↗
NASA NTRS1972

Convolution feedback systems.

Linear time-invariant feedback systems with multiple inputs and multiple outputs are examined. It is demonstrated that no loss of generality takes place considering the feedback to be unity. Necessary and sufficient conditions are derived for the closed-loop impulse response to be stable in a prescribed sense.

Desoer, C. A.↗
NASA NTRS1972

Recent results in convolution feedback systems.

Survey of recent results obtained by the authors concerning certain types of multiinput, multioutput feedback systems. The discrete-time case as well as the continuous-time case are considered. In each case three theorems are shown. These give insight into the nature of the relationship between the open-loop operator and the closed-loop operator of the system, as well as necessary and sufficient conditions for stability of the closed-loop system when 'unstable' poles are present in their open-loop transfer function.

Desoer, C. A.↗
NASA NTRS1972

L2-stability of distributed feedback systems: Singular perturbation

A continuous time, single input-single output, linear, time-invariant, distributed feedback system F sup epsilon, containing a small delay of length epsilon in the loop, is considered. Conditions are given under which L2-stability and L2-instability of this feedback system can be deduced from those of the reduced model obtained by neglecting the delay. The two system models associated with F sup epsilon are the low-frequency model F and the high frequency model F. The condition for neglecting the small delay is the L2-stability of the family of high-frequency models, where epsilon or = 0 is sufficiently small. A lemma and a theorem are given. The lemma gives sharp Nyquist-type conditions for the L2-stability and L2-instability of the family of high frequency models for sufficiently small epsilon or = 0, while the Theorem gives explicit conditions under which the small delay may or may not be neglected.

Barman, J. F.↗