We give detailed discussion of a procedure for determining the robust -stability of a real matrix. The procedure begins from the Hurwitz stability criterion. The procedure is applied to two numerical examples.
In this paper, we propose a new impulsive predator prey model with impulsive control at different fixed moments and analyze its interesting dynamic behaviors. Sufficient conditions for the globally asymptotical stability of the semi-trivial periodic solution and the permanence of the present model are obtained by Floquet theory of impulsive differential equation and small amplitude perturbation skills. Existences of the "infection-free" periodic solution and the "predator-free" solution are analyzed...
The purpose of this paper is to show that the method of controlled lagrangians and its hamiltonian counterpart (based on the notion of passivity) are equivalent under rather general hypotheses. We study the particular case of simple mechanical control systems (where the underlying lagrangian is kinetic minus potential energy) subject to controls and external forces in some detail. The equivalence makes use of almost Poisson structures (Poisson brackets that may fail to satisfy the Jacobi identity)...
The purpose of this paper is to show that the method of controlled Lagrangians and its Hamiltonian counterpart (based on the notion of passivity) are equivalent under rather general hypotheses. We study the particular case of simple mechanical control systems (where the underlying Lagrangian is kinetic minus potential energy) subject to controls and external forces in some detail. The equivalence makes use of almost Poisson structures (Poisson brackets that may fail to satisfy the Jacobi identity)...
We study the dynamical properties of a plane engine vibrations modelled by a system of ODE.
Let be a real Hilbert space, a convex function of class that we wish to minimize under the convex constraint . A classical approach consists in following the trajectories of the generalized steepest descent system (cf. Brézis [5]) applied to the non-smooth function . Following Antipin [1], it is also possible to use a continuous gradient-projection system. We propose here an alternative method as follows: given a smooth convex function whose critical points coincide with and a control...
Let H be a real Hilbert space, a convex function of class that we wish to minimize under the convex constraint S. A classical approach consists in following the trajectories of the generalized steepest descent system (cf. Brézis [CITE]) applied to the non-smooth function . Following Antipin [1], it is also possible to use a continuous gradient-projection system. We propose here an alternative method as follows: given a smooth convex function whose critical points coincide with S and...