Abstract: An important technique in stability theory for
differential equations is known as the direct method of Lyapunov. In
this work we deal global stability properties of Leptospirosis
transmission model by age group in Thailand. First we consider the
data from Division of Epidemiology Ministry of Public Health,
Thailand between 1997-2011. Then we construct the mathematical
model for leptospirosis transmission by eight age groups. The
Lyapunov functions are used for our model which takes the forms of
an Ordinary Differential Equation system. The globally
asymptotically for equilibrium states are analyzed.
Abstract: In this paper, the trajectory tracking problem for carlike mobile robots have been studied. The system comprises of a leader and a follower robot. The purpose is to control the follower so that the leader-s trajectory is tracked with arbitrary desired clearance to avoid inter-robot collision while navigating in a terrain with obstacles. A set of artificial potential field functions is proposed using the Direct Method of Lyapunov for the avoidance of obstacles and attraction to their designated targets. Simulation results prove the efficiency of our control technique.
Abstract: In this paper, the decomposition-aggregation method
is used to carry out connective stability criteria for general linear
composite system via aggregation. The large scale system is
decomposed into a number of subsystems. By associating directed
graphs with dynamic systems in an essential way, we define the
relation between system structure and stability in the sense of
Lyapunov. The stability criteria is then associated with the stability
and system matrices of subsystems as well as those interconnected
terms among subsystems using the concepts of vector differential
inequalities and vector Lyapunov functions. Then, we show that the
stability of each subsystem and stability of the aggregate model
imply connective stability of the overall system. An example is
reported, showing the efficiency of the proposed technique.