On the Discrete-time Bounded Real Lemma with application in the characterization of static state feedback H ∞ controllers

This short paper extends the existence theory of the stabilizing solution of the discrete algebraic Riccati equation. The main result provides necessary and sufficient conditions for the existence of such a solution, free of any a priori conditions on the problem data. For the special case of the optimal regulator problem, standard results are recovered as special cases.

The stabilizing solution of the discrete algebraic riccati equation

We develop controller synthesis algorithms for decentralized control problems, where individual subsystems are connected over a network. We focus on the simplest information structure, consisting of two interconnected linear systems, and construct the optimal controller subject to a decentralization constraint via a spectral factorization approach. We provide explicit state-space formulae for the optimal controller, characterize its order, and show that its states are those of a particular optimal estimator.

An explicit state-space solution for a decentralized two-player optimal linear-quadratic regulator

The continued fraction and time-moments methods for the reduction in order of linear continuous-time systems are extended for use in reducing the order of linear discrete-time systems- Simple numerical examples are given to illustrate the methods

Continued fraction methods for the reduction of discrete-time dynamic systems

Papers on optimal, control theory, reviewed in Referativnyi Zhurnal “Matematika” during 1971–1975, are surveyed.

Mathematical theory of optimal control

A z transform factorisation result is developed from the discrete-time matrix Riccati equation, in a similar way to the well known spectral-factorisation result of continuous time systems.

Factorisation result for optimal discrete-time systems

The method of moments is used to fit a pulse transfer function of given order r to a given sampled impulse-response function. By this means, the model correctly predicts the system response to an arbitrary polynomial input of order 2r?1, and correctly predicts the required polynomial input to correct for additive polynomial drift at the output of order 2r?1.

Approximation of a sampled impulse-response function by a pulse transfer function

The use of dyadic feedback to simplify matrix manipulations in multivariable-control-system design has been recognised. Some of these results are combined in a root-locus procedure to give positive guidance in the selection of feedback coefficients.

D.H. Mee

Papers

Factorisation result for optimal discrete-time systems

Approximation of a sampled impulse-response function by a pulse transfer function

Use of unity-rank output feedback to guide the selection of feedback coefficients