The relation between the solvability of the disturbance decoupling problem for a nonlinear system and its linearization around a working point is investigated. It turns out that generically the solvability of the disturbance decoupling via regular dynamic state feedback is preserved under linearization. This result gives a partial interpretation of introducing integral action in classical PID-c...

Recently a moving boundary approximation for the minimal model for negative streamer ionization fronts was extended with effects due to front curvature; this was done through a systematic solvability analysis. A central prediction of this analysis is the existence of a nonvanishing electric field in the streamer interior, whose value is proportional to the front curvature. In this paper we comp...

Given a Petri net N = (P, T, E), a siphon is a set S of places such that the set of input transitions to S is included in the set of output transitions from S. Concerning extraction of one or more minimal siphons containing a given specified set Q of places, the paper shows several results on polynomial time solvability and NP -completeness, mainly for the case |Q| ≥ 1. key words: Petri nets, m...

3 Semilinear equations with absorption 19 3.1 The Marcinkiewicz spaces approach . . . . . . . . . . . . . . . . . . . . . . 20 3.2 Admissible measures and the ∆2-condition . . . . . . . . . . . . . . . . . . . 26 3.3 The duality method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.3.1 Bessel capacities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.3.2 Sharp...

It is proved that applying sufficient regularity conditions to the interval matrix [A − |B|, A + |B|], we can create a new unique solvability condition for the absolute value equation Ax + B|x| = b, since regularity of interval matrices implies unique solvability of their corresponding absolute value equation. This condition is formulated in terms of positive definiteness of a certain point mat...

Solvability issues of four boundary value problems for a nonlocal biharmonic equation in the unit ball are investigated. Dirichlet, Neumann, Navier and Riquier–Neumann studied. For under consideration, existence uniqueness theorems proved. Necessary sufficient conditions solvability all obtained an integral representations solutions given terms corresponding Green’s functions.

In this paper we formulate and study the uniform global output regulation problem for systems with discontinuous right-hand sides. A characterization of all controllers solving this problem is provided. Based on this characterization, the regulator equations for discontinuous systems are derived. Solvability of these regulator equations is a necessary condition for the solvability of the unifor...

This paper deals with the problems of checking strong solvability and feasibility of linear interval equations, checking weak solvability of linear interval equations and inequalities, and finding control solutions of linear interval equations. These problems are known to be NP -hard. We use some recently developed characterizations in combination with classical arguments to show that these pro...

Nonimprovable in a certain sense, sufficient conditions for the solvability and unique solvability of the problem u′(t) = F (u)(t), u(a)− λu(b) = h(u) are established, where F : C([a, b];R) → L([a, b];R) is a continuous operator satisfying the Carathéodory condition, h : C([a, b];R) → R is a continuous functional, and λ ∈ R+. 2000 Mathematics Subject Classification: 34K10.

In their classical work, Ladyzhenskaya and Ural′tseva gave a definition of weak solution for parabolic equations in cylindrical domains. Their definition was broad enough to guarantee the solvability of all such problems but narrow enough to guarantee the uniqueness of these solutions. We give here some alternative definitions which are appropriate to non-cylindrical domains, and we prove the u...