Large scale control systems results of multivariable feedback systems models and structure of interconnected systems decentralized stabilizability the decentralized stabilization and pole assignment optimal decentralized control stability analysis of interconnected systems decentralized design for strongly coupled subsystems decentralized design for weakly coupled systems decentralized PI controllers strongly coupled symmetric composite systems survey of the results and open problems in feedback control of large-scale systems.

Feedback control of large-scale systems

Decentralized design of feedback control for large-scale systems

A quasi-LMI approach to computing stabilizing parameter ranges of multi-loop PID controllers

The current interest in robust control has called into question the applicability of the quantitative feedback theory (QFT) robust design method introduced by Horowitz. A number of issues have been raised regarding inherent restrictions of both the design method and the uncertain plant set. Using a multivariable root-locus technique extended to uncertain systems, this paper shows that the QFT assumptions are indeed not restrictive and are in fact equivalent to other well-known conditions for robust stabilizability. Because QFT is one of the very few methods to specifically address the quantitative robust performance issue, these results should lead to better methods of developing new QFT-design software, as well as improved robust control methods to satisfy a priori quantitative performance bounds.

Algebraic and topological aspects of quantitative feedback theory

In this paper, the design of multivariable proportional-integral-derivative (PID) controllers for discrete-time systems based on linear matrix inequalities (LMIs) is studied. First the stability problem of the closed-loop system with the multivariable PID controller is investigated. To adjust the transient response of the resulting closed-loop system, the design method is extended to account for a pole clustering constraint. PID controller design methods that yield closed-loop systems with H∞ and H2 performance specifications are then investigated. Algorithms based on properly formulated LMIs are developed for the above different cases. Finally, the performance of the proposed controllers is experimentally evaluated in an adaptive optics system where it is desired to control the shape of a magnetic fluid deformable mirror. The experimental results indicate the proposed controllers can successfully provide the desired shape tracking performance in the closed-loop adaptive optics system.

LMI-Based Multivariable PID Controller Design and its Application to the Control of the Surface Shape of Magnetic Fluid Deformable Mirrors

This paper gives bounds for the inverse transfer function.between the jth input-output pair in an n × n multivariable feedback system when the jth loop is open and all other loops k≠ j are closed. Choice of the minimal such bounds are also studied as well as the effect of feedback gains on these bounds. These results are useful in the design of linear multi variable systems.

The convergence and local minimality of bounds for transfer functions

A general criterion is presented for establishing the stability of a multivariable system from the stability of the simplified system consisting of its diagonal elements. This new criterion includes all known criteria of stability based on the diagonal system elements such as Rosenbrock's (1974), Nwokah's (1980) anil Koussiouris's (1980). For the class of matrices satisfying this criterion an equivalent result in terms of eigenloci can also be stated

The stability of linear multivariable systems

Estimates for the inverse of a matrix and bounds for eigenvalues

Methods of decomposing the stability problem of a multivariable feedback system to a number of single loop stability subproblems are useful from a designer' s viewpoint because they enable multivariable design to be effected by a succession of single loop designs. Some results which make this possible are given here and are natural generalizations of those of Rosenbrock.

A note on the stability of multivariable systems

A large number of papers have appeared in recent years on the use of generalized row sums and generalized column sums in the extended version of the Rosenbrock Nyquist Array design scheme for multivariable systems Some of the authors claim that their results using these row/ column sums encompass similar results using the Hadamard property of irreducible complex matrices It is the purpose of this note to indicate that such claims are false On the contrary, all these results are direct consequences of the Hadamard property and can be deduced from standard results in M-matrix theory

O. D. I. Nwokah

Papers

The convergence and local minimality of bounds for transfer functions

The stability of linear multivariable systems

Estimates for the inverse of a matrix and bounds for eigenvalues

A note on the stability of multivariable systems

A recurrent issue on the extended Nyquist Array