A new robust Strictly Positive Real Synthesis Toolbox (SPRSt) for use with Matlab has been developed. Some algorithms for robust Strictly Positive Real Synthesis are introduced briefly and the use of the toolbox is illustrated by several examples. At last a link to downloadable code is provided.

We prove results concerning the interlacing of eigenvalues of principal submatrices of strictly totally positive (STP) matrices.

In this talk we will advocate the use of weak systems of modal logic called strictly positive. These can be seen as fragments of polymodal logic consisting of implications of the form A → B, where A and B are formulas built-up from T (truth) and the variables using just conjunction and the diamond modalities. The interest towards such fragments independently emerged around 2010 in two different...

In this paper it is shown that the intuitionistic fixed point theory ÎD i α(strict) for α times iterated fixed points of strictly positive operator forms is conservative for negative arithmetic and Π2 sentences over the theory ACA−i α for α times iterated arithmetic comprehension without set parameters. This generalizes results previously due to Buchholz [5] and Arai [2].

Recursive domain equations have natural solutions. In particular there are domains defined by strictly positive induction. The class of countably based domains gives a computability theory for possibly non-countably based topological spaces. A qcb0 space is a topological space characterized by its strong representability over domains. In this paper, we study strictly positive inductive definiti...

Abstract. If f(t) = ∑∞ k=0 akt k converges for all t ∈ IR with all coefficients ak ≥ 0, then the function f(< x,y >) is positive definite on H ×H for any inner product space H. Set K = {k : ak > 0}. We show that f(< x,y >) is strictly positive definite if and only if K contains the index 0 plus an infinite number of even integers and an infinite number of odd integers.

Exploratory tools that are sensitive to arbitrary statistical variations in spike train observations open up the possibility of novel neuroscientific discoveries. Developing such tools, however, is difficult due to the lack of Euclidean structure of the spike train space, and an experimenter usually prefers simpler tools that capture only limited statistical features of the spike train, such as...

Let Ai (i = 1,2, · · · ,k) be bounded linear operators on a Hilbert space. This paper aims to show a characterization of operator order Ak Ak−1 · · · A2 A1 > 0 in terms of operator inequalities. Afterwards, an application of the characterization is given to operator equalities due to Douglas’s majorization and factorization theorem. Mathematics subject classification (2010): 47A63.

In this paper, the authors present a linear matrix inequality (LMI) approach to the strictly positive real (SPR) synthesis problem: find an output feedback K such that the closed-loop system T (s) is SPR. The authors establish that if no such constant output feedback K exists, then no dynamic output feedback with a proper transfer matrix exists to make the closed-loop system SPR. The existence ...