The effect of infinitesimal damping on the dynamic instability mechanism of conservative systems.
The equivalence of controlled lagrangian and controlled hamiltonian systems
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 Equivalence of Controlled Lagrangian and Controlled Hamiltonian Systems
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 geometry of convex cones associated with the Lyapunov inequality and the common Lyapunov function problem.
The linearized uniform asymptotic stability of evolution differential equations
The Lyapunov stability for the linear and nonlinear damped oscillator with time-periodic parameters.
The Lyapunov stability of the Timoshenko type equation
The Region of Attraction of the Zero Solution of y' (t) = - (y(t-1)) 2m+1.
The strict stability of dynamic systems on time scales.
The structural influence of the forces of the stability of dynamical systems.
Topological dynamics and the extension of Lyapunov's method
Total separation and asymptotic stability.
Total stability properties based on fixed point theory for a class of hybrid dynamic systems.
Total stability property in limiting equations for a functional-differential equation with infinite delay