Abstract With a scalar potential and bivector potential, the vector field associated with drift of diffusion is decomposed into generalized gradient field, perpendicular to gradient, divergence-free field. We give such decomposition probabilistic interpretation by introducing cycle velocity from bivectorial formalism nonequilibrium thermodynamics. New understandings on mean rates thermodynamic ...

In this paper, we present a novel approach to determine the stability of switched linear and nonlinear systems using Sum Squares optimisation. Particularly, use optimisation search for Lyapunov function that defines an absorbing set confines solution trajectories. For systems, show also implies global asymptotic stability. Using approach, can study broader range particularly, attractor whose dy...

The Lyapunovmethod for stability analysis of an equilibrium state of a nonlinear dynamic system requires a Lyapunov function v(t, x) having the following properties: (1) v is a positive definite function, and (2) v̇ is at least a negative semi-definite function. Finding such a function is a challenging task. The first theorem presented in this paper simplifies the second property for a Lyapunov ...