Showing papers by "Brian D. O. Anderson published in 1986"

Robust model reference adaptive control

Abstract: We propose a new model reference adaptive control algorithm and show that it provides the robust stability of the resulting closed-loop adaptive control system with respect to unmodeled plant uncertainties. The robustness is achieved by using a relative error signal in combination with a dead zone and a projection in the adaptive law. The extra a priori information needed to design the adaptive law, are bounds on the plant parameters and an exponential bound on the impulse response of the inverse plant transfer function.

Stability and the matrix Lyapunov equation for discrete 2-dimensional systems

Abstract: The stability of two-dimensional, linear, discrete systems is examined using the 2-D matrix Lyapunov equation. While the existence of a positive definite solution pair to the 2-D Lyapunov equation is sufficient for stability, the paper proves that such existence is not necessary for stability, disproving a long-standing conjecture.

Controller reduction via stable factorization and balancing

Abstract: A controller reduction procedure based on a representation of a controller as a matrix function defined using stable proper transfer functions and employing a balancing technique is studied in this paper. For a certain right coprime factorization of an LQG designed controller K(s) = N(s)D-1(s), we approximate using a balancing technique the pair [D(s), N(s)]T by a low-order pair [D1(s), N1(s)]T defining a factorization of the reduced-order controller K 1(s) = N1(s)D1 -1(s). We show that reducing the controller order in this way is motivated in a natural way, which leads to the expectation of both good stability properties and good accuracy of approximation of closed-loop behaviour. This is also demonstrated in some examples.

Output-error identification methods for partially known systems

Abstract: Output-error methods are applied to the problem of identifying partially known linear time-invariant finite-dimensional systems. The systems considered have a limited number of unknown parameters, ...

q-Markov covariance equivalent realizations

Abstract: This paper describes a class of reduced order models which match both the first q Markov Parameters and the first q Output Covariances for linear systems subject to white noise inputs. The class of reduced models contains the earlier models [2] as a special case.

The approximation of power spectra by phase matching

Abstract: We consider the problem of approximating high order multivariable power spectra by lower order power spectra using the phase matching approach of Jonckheere, Helton and Harshavadhana [1,2,3]. The motivation for the phase matching approach is the identification [1,2,3] of the Hankel operator associated with the "phase function" as Akaike's canonical correlation operator [4]. Thus the phase matching approach can also be viewed as an algorithm for the approximate realization of a stochastic process by canonical variables, which is desirable for the implementation of an approximate Kalman filter of the power spectrum.

A local stability analysis for a class of adaptive systems

Abstract: An analysis of adaptive systems is presented where a local L_{\infty} -stability is ensured under a persistent excitation condition.

A summary of recent results on the scalar rational interpolation problem

Abstract: A summary of the results on the scalar rational interpolation problem obtained in ANTOULAS and ANDERSON [1986] is presented.