Quadratic stabilization of a class of linear systems and its application to robot control

Abstract

In this paper, we consider the simultaneous quadratic stabilization problem for a class of linear time-invariant (LTI) systems. It has been shown that a set of LTI systems in block companion form is simultaneously quadratically stabilizable by a single static state feedback controller. Based on this result, a new approach to robot tracking controller design is presented. The proposed control scheme consists of a feedforward controller based on the inverse dynamics of the robot and a feedback controller. The nonlinear model of the robot is viewed as piecewise LTI systems obtained by linearizing the model at selected number of points on a specified trajectory in the joint space. The collection of all the LTI systems constitutes a set in which each member is observed to be in block companion form. For this class of systems, an algorithm for the design of a single stabilizing feedback controller is presented. A numerical example of a two link manipulator has been considered to validate the proposed theory.