Advanced Statistical Methods in Biometric Research.

An algorithm is presented in this paper for computing state-space balancing transformations directly from a state-space realization. The algorithm requires no "squaring up" or unnecessary matrix products. Various algorithmic aspects are discussed in detail. A key feature of the algorithm is the determination of a contragredient transformation through computing the singular value decomposition of a certain product of matrices without explicitly forming the product. Other contragredient transformation applications are also described. It is further shown that a similar approach may be taken, involving the generalized singular value decomposition, to the classical simultaneous diagonalization problem. These SVD-based simultaneous diagonalization algorithms provide a computational alternative to existing methods for solving certain classes of symmetric positive definite generalized eigenvalue problems.

Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms

Robust Control Design with MATLAB (second edition) helps the student to learn how to use well-developed advanced robust control design methods in practical cases. To this end, several realistic control design examples from teaching-laboratory experiments, such as a two-wheeled, self-balancing robot, to complex systems like a flexible-link manipulator are given detailed presentation. All of these exercises are conducted using MATLAB Robust Control Toolbox 3, Control System Toolbox and Simulink. By sharing their experiences in industrial cases with minimum recourse to complicated theories and formulae, the authors convey essential ideas and useful insights into robust industrial control systems design using major H-infinity optimization and related methods allowing readers quickly to move on with their own challenges. The hands-on tutorial style of this text rests on an abundance of examples and features for the second edition: rewritten and simplified presentation of theoretical and methodological material including original coverage of linear matrix inequalities; new Part II forming a tutorial on Robust Control Toolbox 3; fresh design problems including the control of a two-rotor dynamic system; and end-of-chapter exercises. Electronic supplements to the written text that can be downloaded from extras.springer.com/isbn include: M-files developed with MATLAB help in understanding the essence of robust control system design portrayed in text-based examples; MDL-files for simulation of open- and closed-loop systems in Simulink; and a solutions manual available free of charge to those adopting Robust Control Design with MATLAB as a textbook for courses. Robust Control Design with MATLAB is for graduate students and practising engineers who want to learn how to deal with robust control design problems without spending a lot of time in researching complex theoretical developments.

Robust control design with MATLAB

Singular perturbations and time-scale methods in control theory: Survey 1976-1983

Computer Solution of Linear Algebraic Systems. By G. Forsythe and C. B. Moler. Pp. xi, 148. 1967. (Prentice-Hall.)

A new zero-order singular perturbational type approximation is developed for model reduction of discrete-time linear systems. This approximation is also suitable for model reduction of systems which have fast subsystems and which are represented in the internally balanced format. Subsystem elimination as suggested by Moore for continuous-time systems does not generalize for the discrete-time case, and the singular perturbational approximation gives a particular solution to the discrete-time internally balanced model reduction problem.

Singular perturbational approximations for discrete-time balanced systems

Singular perturbational approximations for linear continuous-time and discrete-time systems are developed in the frequency domain. It is shown that the familiar singular perturbational result is an approximation at the origin in the complex plane. However, if the system has multiple time-scale effects, other approximations can be obtained at different locations on the negative real axis to emphasize such behavior. The relationship between singular perturbational approximations and direct subsystem elimination is also investigated.

Singular perturbational model reduction in the frequency domain

A new test for minimality of single-input single-output state-space realizations is proposed based on rank conditions of a cross-Gramian type matrix without computing the controllability and observability Gramian matrices.

http://ieeexplore.ieee.org/iel5/5/31318/01456728.pdf

Minimality of SISO linear systems

The Cauchy index for linear SISO systems is given by the signature of the cross-Gramian matrix W co defined by Fernando and Nicholson [1]. This index is useful in the qualitative understanding of systems, and the importance of this index in internally balanced model reduction is illustrated.

https://ieeexplore.ieee.org/iel5/9/24198/01103200.pdf

On the Cauchy index of linear systems

The double-sided form of the Karhunen-Loeve expansion based on the singular value decomposition of matrices is developed. It has applications in data analysis, contraction and prediction in two-dimensional processes.

K.V.M. Fernando

Papers

Singular perturbational approximations for discrete-time balanced systems

Singular perturbational model reduction in the frequency domain

Minimality of SISO linear systems

On the Cauchy index of linear systems

Discrete double-sided Karhunen-Loève expansion