Derivative Feedback Control for a Class of Uncertain Linear Systems Subject to Actuator Saturation

• Published in: Journal of control, automation & electrical systems Vol. 30; no. 4; pp. 490 - 500
• Main Authors: Wolmuth, Leidy Diane, Alves, Uiliam Nelson Lendzion Tomaz, Teixeira, Marcelo Carvalho Minhoto, Assunção, Edvaldo, Cardim, Rodrigo, Moreira, Manoel Rodrigo
• Format: Journal Article
• Language: English
• Published: New York Springer US 15.08.2019; Springer Nature B.V
• Subjects: Actuators; Control; Control and Systems Theory; Control systems; Decay rate; Dynamic stability; Dynamics; Electrical Engineering; Engineering; Feedback control; Initial conditions; Linear matrix inequalities; Linear systems; Mathematical analysis; Matrix methods; Mechatronics; Robotics; Robotics and Automation; Saturation; State vectors; Linear matrix inequalities; Actuator saturation; Derivative feedback; Uncertain linear system
• ISSN: 2195-3880; 2195-3899
• DOI: 10.1007/s40313-019-00474-x

This manuscript considers a class of linear systems with time-invariant uncertainties, where only the derivative of the state vector is considered for feedback. In this scenario, the proposed strategy uses auxiliary dynamics, whose state is accessible for feedback, to control the original plant. It is proposed a design procedure by means of linear matrix inequalities, adding an auxiliary dynamics and subject to actuator saturation. If the conditions are feasible, they assure that the equilibrium point of the closed-loop system is locally asymptotically stable, for all initial conditions in an ellipsoidal region, which is within a given region defined for the plant and the new dynamics. Although the proposed design includes an auxiliary dynamics, it ensures the stability and decay rate proprieties for the original plant. Simulations examples illustrate the effectiveness of the proposed approach.