Nobuhide Suda

H ∞ control for descriptor systems: a matrix inequalities approach

Abstract This paper considers the H ∞ control problem for descriptor systems that possibly have impulsive modes and/or jω-axis zeros. First, we propose matrix inequalities that give a generalized stability condition and an H ∞ norm condition for descriptor systems. Using these matrix inequalities, we show that the solvability of a set of matrix inequalities is necessary and sufficient to the existence of a proper controller that satisfies a prescribed H ∞ norm condition as well as stabilizing the closed-loop system and eliminating all impulsive modes. These inequalities are equivalent to certain linear matrix inequalities, to which we can get solutions whenever they exist using efficient polynomial-time algorithms.

LMI‐based controller synthesis: A unified formulation and solution

This paper proposes a unified approach to linear controller synthesis that employs various LMI conditions to represent control specifications. We define a comprehensive class of LMIs and consider a general synthesis problem described by any LMI of the class. We show a procedure that reduces the synthesis problem, which is a BMI problem, to solving a certain LMI. The derived LMI condition is equivalent to the original BMI condition and also gives a convex parametrization of all the controllers that solve the synthesis problem. The class contains many of widely-known LMIs (for H∞ norm, H2 norm, etc.), and hence the solution of this paper unifies design methods that have been proposed depending on each LMI. Further, the class also provides LMIs for multi-objective performance measures, which enable a new formulation of controller design through convex optimization.

Dualistic differential geometry of positive definite matrices and its applications to related problems

Abstract Analysis on the set of positive definite matrices is involved in many engineering problems. We develop a differential geometric theory of the set of positive definite matrices by means of a specific class of connections introduced into it. Consequently, various dualistic aspects of the set are elucidated. Next, using the theory, we derive new results and interesting geometrical interpretations for matrix approximation, positive definite matrix completion, and linear matrix inequality problems.

LMI-based output feedback controller design-using a convex parametrization of full-order controllers

This paper proposes a unified output feedback controller synthesis method that employs LMI-represented specifications of H/sub 2/ norm control, H/sub /spl infin// norm control, root clustering and various multiobjective performances. For this purpose, we show a new parametrization of full-order controllers with a convex parameter set, and reduce synthesis problems to solving an LMI on the parameter space.

Invariant zeros and input-output structure of linear, time-invariant systems

We define the concepts of conditional reachability and observability. Necessary and sufficient conditions are obtained for a linear, time-invariant system to be conditionally reachable and observable. Some new results on the perfect reachability and observability are also presented. It is shown that the rank of the transfer function matrix and the geometric multiplicity of the invariant zeros play a key role in these conditions.

A Theory of Reactor Diagnosis in Feedback Systems

A unified theory is presented for diagnosis of power reactors with feedback mechanism. In terms of correlation functions calculated from stationary time series data, a feedback system can be expressed by an equivalent innovation model. From the formalism the identifiability of open loop transfer functions in the feedback system is discussed under conditions; (1) the minimum phase system, (2) the independence of noise sources. From the feedback structure, the property of the nonminimum phase is related to that the reactivity is positive or zero-power reactor transfer function is supercritical. In the case of the nonminimum phase and correlated noise sources, there is a possibility of new additional loops in an innovation model equivalent to the feedback system.

ESTIMATION OF REACTOR PARAMETERS BY OPTIMAL FILTERING METHOD.

Measurements of reactor parameters, such as prompt neutron generation time and subcriticality, have been made in the past using band pass filters or else applying the correlation technique. Other new methods of reactor parameter estimation would now appear to be available thanks to the recent developments in optimal filtering technique, such as optimal linear (Kalman) filter and some of the nonlinear optimal filters. Such new methods should prove very promising for on-line estimation of the reactor parameters. In this paper a description is given of the application of some of these new methods to subcriticality measurements. The results of computer simulation of estimates using the Kalman filter are presented, as also on account of experiments with the actual reactor noise obtained on the Toshiba Training Reactor (TTR-1), using a nonlinear analog filter. The results agreed with those reported by Nomura using conventional methods.

Decoupling of Nonsquare Systems — a Necessary and Sufficient Condition in Terms of Infinite Zeros

Abstract We discuss the decoupling or nonint eract ing control of nonsquare systems, that is systems having more inputs than out puts, by state feedback. The multiplicities of the infinite zeros of the system, representing its internal structure, play an important role and the problem of decoupling is reduced to that of appropriately assigning the multiplicities of the infinite zeros. By this approach, a necessary and sufficient condition for decoupling of nonsquare systems is determined. An algorithm for decoupling is also presented.

Robust multi-objective controller design via convex optimization

This paper proposes a robust multi-objective controller design approach that employs a large class of LMI-conditions to represent design goals. First, we define a comprehensive class of LMIs, and present a solution to synthesis problems to satisfy and any of the LMIs in the class for nominal plants. Then, this result is applied to plants with norm-bounded uncertainties.

Reactor noise analysis. Recent research activities in Japan.

A review is presented on the recent research activities in Japan in the field of reactor noise analysis. It covers six selected areas : nonlinear stochastic theory and identification of nonlinearit...