Hideki Kokame

Convergence property of interval matrices and interval polynomials

In association with robust control-system design and analysis, the Hurwitz property of interval matrices and interval polynomials has recently been actively investigated. However, its discrete counterpart, the convergence property, has seemingly not been much discussed. In this paper, this property is studied in comparison with the Hurwitz counterpart. Some conditions under which interval matrices or interval polynomials are convergent are derived.

A necessary and sufficient condition for stability of linear discrete systems with parameter-variation

Abstract A simple sufficient stability criterion for linear discrete systems obtained previously is proved to be necessary and sufficient for the stability of a class of such systems with parameter-variation.

A root distribution criterion for interval polynomials

The problem of finding the conditions under which an interval polynomial has a given number of roots in the open left-half plane and the other roots in the open right-half plane, irrespective of the values of its coefficients, is considered. A simple criterion is provided to test interval polynomials for the root distribution invariance, viewed as an extension of Kharitonovs theorem. The goal is to provide an alternative theorem and then give an efficient means of checking the root distribution invariance. >

Stabilization of perturbed systems via linear optimal regulator

Linear quadratic state feedback regulators make the resulting closed-loop systems stable enough, i.e. they realize robust stabilization. Many attempts at robust stabilization using linear quadratic regulators have been reported. One of the major trends of formulating uncertainty in systems is to express perturbed parameters as the sum of two terms, i.e. nominal values and the deviation from them. In this paper, it is assumed that the upper and lower bounds for each uncertain parameter can somehow be estimated. This enables us to dispense with nominal values. The main aim is to contrive a robust feedback stabilization law for systems with parameters falling into certain ranges via a linear quadratic regulator based only upon information on their bounds. The systems under consideration are therefore those having interval system matrices (in which each element has the above-mentioned two-sided bounds). A certain feedback law is a stabilizing law for a system with an interval system matrix if and only if the ...

An exact quadratic stability condition of uncertain linear systems

It is pointed out that in order to check the quadratic stability of a family of linear systems with a stable nominal system, the positive definiteness constraint can be dropped from the quadratic Lyapunov function. >

Entire family of convex directions for real Hurwitz matrices

Relating to end point results for the stability of segment polynomials, Rantzer (1992) has studied the convex direction and has completely characterized it. By extending this new concept to the matrix case, the present paper discloses the entire family of convex directions for the case of real Hurwitz matrices.<<ETX>>

A Branch and Bound Method to Check the Stability of a Polytope of Matrices

The stability of a linear time-invariant system which has uncertain parameters is often reduced to the stability of a polytope of matrices. To determine whether the matrix polytope is stable or not, the present paper proposes a branch and bound method which is based on the polytopic Lyapunov functions approach. The stability criterion involved is obtained from evaluating a lower bound of degree of stability. A matrix which attains the lower bound might be anticipated to give the worst degree of stability. Thus we check the instability of such an element matrix. Some examples are shown to illustrate the performance of our method.

A polytopic quadratic Lyapunov functions approach to stability of a matrix polytope

It is known that a polytope of matrices is stable if there exists a positive-definite quadratic function that is a Lyapunov function common to all the vertex members. This simple criterion is extended to the case where a multituple of positive-definite quadratic functions is available. Some classes of such multituples that ensure the stability of the polytope are defined. Their inclusion relation is clarified. It is shown that one of the classes provides an easy-to-compute criterion for the stability of a matrix polytope. A systematic use of the criterion is demonstrated by an example concerning the stability of a linear system with unknown parameters.<<ETX>>

Aperiodicity conditions for Polynomials With Uncertain Coefficient Parameters

Aperiodicity is normally defined as a property such that all the roots are simple and negative real, while interval polynomials are referred to as polynomials with coefficients lying within specified closed intervals on the real axis. Several conditions for aperiodicity, including an exact one, are derived. Comments on these conditions are given in contrast to the work of Soh and Berger, who also considered the problem with a modified definition of aperiodicity.

Extended Kharitonov's Theorems and their Application

An attempt is made to extend the well-known Kharitonovs Theorem, which deals with the Hurwitz property of interval polynomials. The extension is carried out in such a manner that the strict Hurwitz property in the original theorem is weakended so that the imaginary axis is incorporated. As a tool for this, the extension is also made for a classical stability criterion, Mikahilovs Theorem, for which a close look into certain limiting processes is made. As a result of the inspection, several theorems concerning the location of the zeros of interval polynomials are obtained. These results are applied to the robustness problems of positive- realness and strict positive realness for given rational functions with interval coefficients.