Stephen L. Campbell

Continuity properties of the Drazin pseudoinverse

Abstract Let B D denote that Drazin inverse of the n × n complex matrix B . Define the core-rank of B as rank ( B i(B) ) where i (B) is the index of B . Let j = 1,2,…, and A j and A be square matrices such that A i converges to A with respect to some norm. The main result of this paper is that A j D converges to A D if and only if there exist a j 0 such that core-rank A j =core-rank A for j ⩾ j 0 .

The Drazln inverse and systems of second order linear differential equations

The problem of computing the Drazin inverse of the matrix discussed. The relationship of this problem to second order differential equations is explained and known results given.

Auxiliary signal design for rapid multi-model identification using optimization

Under the assumption that one of several given models is the real underlying model of the system, a proper auxiliary signal is defined as an input signal that allows one to select the correct model. It is assumed that there is no knowledge prior to the beginning of the application of the auxiliary signal and that detection is to be done within a specified detection horizon. Under the assumption that the noise energy is bounded, a method for the computation of the minimal energy auxiliary signal is given. The new algorithm extends previous work in that it can handle more than two models and certain types of nonlinearities.

Brief paper: Effects of feedback on active fault detection

In recent years there has been increased interest in the use of active approaches for fault detection. In one of these approaches an auxiliary signal is designed such that over a short period it will reveal a fault not otherwise detectable and do so with as little perturbation of system performance as possible. This method is robust in the sense of guaranteeing the detection of the fault for a whole set of bounded uncertainties. Feedback plays an important role in control but its role in active fault detection based on auxiliary signals has not been explored, yet. This paper begins that investigation.

A second order singular linear system arising in electric power systems analysis

Abstract The linear system Mx¨ + (∝ M+ β) K)[xacute] + KX= F with M singular, is decomposed into two linear systems, one singular and one non-singular. The singular ono is solved explicitly in terms of M, K, f, a, S and analysed.

Kalman filtering for general discrete-time LTI systems

Recursive state estimation problems for explicit and implicit time-invariant linear systems, both for systems with and without unknown inputs, can be formulated as a single problem usually referred to as descriptor Kalman filtering. Solutions to this problem have been proposed in the literature, however, these solutions either neglect possible contributions of future dynamics to the current estimate or make unnecessary assumptions on the structure of the system. We propose a solution to this problem which leads to a constructive method lifting these unnecessary assumptions. This method uses a generalization of the shuffle algorithm.

Brief paper: Regularizations of linear time varying singular systems

Singular systems of differential equations arising in reduced-order models are often regularized by the introduction of small parameters. The types of regularization used for linear time invariant systems need not work on linear time varying systems. This paper gives examples and discusses this behavior. Conditions under which the standard type of regularization works are developed.

Rapid Model Selection and the Separability Index

Abstract Under the assumption that one of two given models is the real underlying model of the system, a proper auxiliary signal is defined as an input signal that allows one to select the correct model. It is assumed that there is no knowledge prior to the beginning of the application of the auxiliary signal and that detection is to be done within a specified detection horizon. Under the assumption that the noise energy is bounded, the separability index is defined as the least energy of a proper auxiliary signal. A method for computation of this index is presented.

Descriptor systems in the 1990s

After briefly summarizing the growth in the theory of descriptors, or differential algebraic equations (DAEs), over the last two decades, the current challenges and potential successes are discussed. Among these major challenges facing DAE theory are: numerical software for index 3 systems; implicit Runge-Kutta code for low index problems; boundary value problem numerical codes; linearization; new numerical techniques; the initialization problem; direct control information computing; parameter identification; noisy systems; utilization of constraints; implementation for time invariant control; extra derivatives; large-scale DAEs; real-time simulation: and new types of systems.<<ETX>>

Order and the index of singular time-invariant linar systems*

Various concepts of order have been proposed in the literature. It is shown that many of these are directly related to the index of a system.