The paper deals with the problem of synthesis of a controller to the plant described by Takagi-Sugeno fuzzy model with linear input-output submodels in the consequents of rules. A procedure for design of the controller guaranteeing stability of closed-loop system based on polynomial approach is presented. The controller assignes the same characteristic polynomial for all feasible linear subsyst...

The problem of Finite Settling Time Stabilisation (FSTS) for multivariable, discrete-time systems is discussed in this paper. The approach is algebraic and the problem reduces to the solution of a polynomial Diophantine equation; many of the solvability conditions are expressed as standard linear algebra tests. A Kučera-YoulaBonjiorno type parametrisation of the family of the FSTS controllers i...

We prove the holomorphic linearizability of germs biholomorphisms $$(\mathbb {C}^n,0)$$ , fixing origin, point at which linear part has nontrivial Jordan blocks under following assumptions: eigenvalues are modulus less or equal than 1, non-resonant and satisfy not only a classical Diophantine condition but also new Diophantine-like conditions related to quasi-resonance phenomena.

A central result in the theory of integer optimization states that a system of linear diophantine equations Ax = b has no integral solution if and only if there exists a vector in the dual lattice, yT A integral such that yT b is fractional. We extend this result to systems that both have equations and inequalities {Ax = b, Cx ≤ d}. We show that a certificate of integral infeasibility is a line...

Systems based on the splicing operation are computationally complete. Usually demonstrations of this are based on simulations of type-0 grammars. We propose a diierent way to reach this result by solving Diophantine equations using extended H system with permitting context. Completeness then follows from Matiyasevich's theorem stating that the class of Diophantine sets is identical to the class...

We present the basic concepts and results of Gröbner bases theory for readers working or interested in systems theory. The concepts and methods of Gröbner bases theory are presented by examples. No prerequisites, except some notions of elementary mathematics, are necessary for reading this paper. The two main properties of Gröbner bases, the elimination property and the linear independence prop...

The Polyhedral Escape Problem for continuous linear dynamical systems consists of deciding, given an affine function f : R → R and a convex polyhedron P ⊂ R, whether, for some initial point x0 in P, the trajectory of the unique solution to the differential equation ẋ(t) = f(x(t)),x(0) = x0, t ≥ 0, is entirely contained in P. We show that this problem is decidable, by reducing it in polynomial t...

Linear forms in logarithms have an important role the theory of Diophantine equations. In this paper, we prove explicit [Formula: see text]-adic lower bounds for linear rational numbers using Padé approximations second kind.

In recent years, we have seen several approaches to the graph isomorphism problem based on “generic” mathematical programming or algebraic (Gröbner basis) techniques. For most of these, lower bounds have been established. In fact, it has been shown that the pairs of nonisomorphic CFI-graphs (introduced by Cai, Fürer, and Immerman in 1992 as hard examples for the combinatorial Weisfeiler-Leman a...