QUADRATIC STABILIZATION OF A CLASS OF LINEAR-SYSTEMS AND ITS APPLICATION TO ROBOT CONTROL

In this paper, we consider the simultaneous quadratic stabilization pr oblem for a class of linear time-variant (LTI) systems. It has been sh own that a set of LTI systems in block companion form is simultaneousl y quadratically stabilizable by a single static state feedback control ler. Based on this result, a new approach to robot tracking controller design is presented. The proposed control scheme consists of a feedfo rward controller based on the inverse dynamics of the robot and a feed back controller. The nonlinear model of the robot is viewed as piecewi se LTI systems obtained by linearizing the model at selected number of points on a specified trajectory in the joint space. The collection o f all the LTI systems constitutes a set in which each member is observ ed to be in block companion form. For this class of systems, an algori thm for the design of a single stabilizing feedback controller is pres ented. A numerical example of a two link manipulator has been consider ed to validate the proposed theory.