{'fraction_non_alphanumeric': 0.01263537906137184, 'fraction_numerical': 0.0, 'mean_word_length': 4.898936170212766, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Quadratic stabilization of a class of linear systems and its application to robot control

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.