Stability analysis of uncertain delay differential equations

Uncertain delay differential equation is a class of functional differential equations driven by Liu process. It is an important model to describe the evolution process of uncertain dynamical system. In this paper, on the one hand, the analytic expression of a class of linear uncertain delay differential equations are investigated. On the other hand, the new sufficient conditions for uncertain delay differential equations being stable in measure and in mean are presented by using retarded-type Gronwall inequality. Several examples show that our stability conditions are superior to the existing results.

Adaptive Robust Model-Following Control and Application to Robot Manipulators

The model-following control problem for nonlinear uncertain dynamical systems is considered. Based only on the knowledge of functional properties relating to the bound of the time-varying uncertainty, a class of adaptive feedback controls is developed which, under some realistic assumptions, guarantees the error between the uncertain dynamical system and the model tends to be zero. Application to robotic manipulators is made.