Showing papers by "Takehiro Mori published in 1990"

On the relationship between the spectral radius and stability radius for discrete systems

Abstract: The relationship between the spectral radius and the stability radius is established via elementary calculation. The result gives a discrete counterpart of the existing result for continuous systems and provides an upper bound for the stability radius. The main result of the calculation is summarized in the form of a theorem. >

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

Abstract: 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. >

Aperiodicity and periodicity of interval polynomials

Abstract: Three 'Kharitonov-like regions' for the root location of interval polynomials are indicated. The regions are the imaginary axis, the open left half of the real axis, and the open right half of the real axis. Polynomials whose roots all lie in the open left half real axis are called aperiodic and those with roots only on the imaginary axis, periodic. It is shown that for aperiodicity or periodicity of interval polynomials, checking of the property of only two extreme polynomials is sufficient. Furthermore, the results obtained recover the original Kharitonov theorem. That is, they can provide an alternative way to prove Kharitonov's theorem. >

Aperiodicity conditions for Polynomials With Uncertain Coefficient Parameters

Abstract: 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.