Matrix theory is one of the most fundamental tools of mathematics and science, and a
number of classical books on matrix analysis have been written to explore this theory. As a …

We consider interconnections of n nonlinear subsystems in the input-to-state stability (ISS)
framework. For each subsystem an ISS Lyapunov function is given that treats the other …

We prove an analog of Perron–Frobenius theorem for multilinear forms with nonnegative
coefficients, and more generally, for polynomial maps with nonnegative coefficients. We …

For a nonnegative irreducible tensor, we give distribution properties of its eigenvalues. In
particular, the spectral radius of a nonnegative irreducible tensor with positive trace is …

We show that several decision problems originating from max-plus or tropical convexity are
equivalent to zero-sum two player game problems. In particular, we set up an equivalence …

This is a survey paper on the recent development of the spectral theory of nonnegative
tensors and its applications. After a brief review of the basic definitions on tensors, the H …

When the initial and transition probabilities of a finite Markov chain in discrete time are not
well known, we should perform a sensitivity analysis. This can be done by considering as …

We introduce a general framework for measuring risk in the context of Markov control
processes with risk maps on general Borel spaces that generalize known concepts of risk …

We introduce a new class of nonnegative tensors-strictly nonnegative tensors. A weakly
irreducible nonnegative tensor is a strictly nonnegative tensor but not vice versa. We show …

In this paper, we mainly focus on how to generalize some conclusions from nonnegative
irreducible tensors to nonnegative weakly irreducible tensors. To do so, a basic and …