23 citations · 72 across the 27 of their papers we have counts for
30 papers
Generalized Markov-Bernstein inequalities and stability of dynamical systems
Vladimir Yu. Protasov
The Markov-Bernstein type inequalities between the norms of functions and of their derivatives are analysed for complex exponential polynomials. We establish a relation between the…
The length of switching intervals of a stable linear system
Rinat Kamalov, Vladimir Yu. Protasov
The linear switching system is a system of ODE with the time-dependent matrix taking values from a given control matrix set. The system is (asymptotically) stable if all its trajec…
Stability of linear systems with bounded switching intervals
Vladimir Yu. Protasov, Rinat Kamalov
We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded as from below (the guarantee…
Surface dimension, tiles, and synchronising automata
Vladimir Yu. Protasov
We study the surface regularity of compact sets which is equal to the supremum of numbers such that the measure of the set doe…
The Barabanov norm is generically unique, simple, and easily computed
Vladimir Yu. Protasov
Every irreducible discrete-time linear switching system possesses an invariant convex Lyapunov function (Barabanov norm), which provides a very refined analysis of trajectories. Un…
Antinorms on cones: duality and applications
Vladimir Yu. Protasov
An antinorm is a concave nonnegative homogeneous functional on a convex cone. It is shown that if the cone is polyhedral, then every antinorm has a unique continuous extension from…