Robust guaranteed cost control of linear systems with norm bounded uncertainties and external disturbance

This paper proposes a robust guaranteed cost control method for a linear system with norm bounded time varying parametric uncertainties and external disturbance. Using the Lyapunov stability theory and linear matrix inequality method, a robust guaranteed cost control law is derived to guarantee that the closed loop system is not only stable, but also has adequately quadratic and H∞ performance levels for all the admissible uncertainties and external disturbance. A convex optimization problem is formulated to obtain the optimal state feedback controller which can minimize the quadratic and H∞ performance levels. Based on the model of the robot prototype for inspecting power transmission lines, simulation results verify the effectiveness of the proposed method.

[1]  Chang-Hua Lien,et al.  Robust observer-based control of systems with state perturbations via LMI approach , 2004, IEEE Transactions on Automatic Control.

[2]  Wook Hyun Kwon,et al.  Delay-dependent guaranteed cost control for uncertain state-delayed systems , 2005, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[3]  Adaptive guaranteed cost control of a class of uncertain nonlinear systems , 2007 .

[4]  Ian R. Petersen,et al.  Optimal Guaranteed Cost Control of Uncertain Linear System , 1992, 1992 American Control Conference.

[5]  Yong Wang,et al.  Novel Optimal Guaranteed Cost Control of Uncertain Discrete Systems with Both State and Input Delays , 2008 .

[6]  Shuwen Pan,et al.  LMI approach to reliable guaranteed cost control with multiple criteria constraints: The actuator faults case , 2009 .

[7]  Z. You,et al.  Optimal guaranteed cost control of a class of nonlinear uncertain discrete-time systems: an LMI approach , 2006, 2006 American Control Conference.

[8]  M. Aliyu.  Guaranteed cost control of uncertain nonlinear systems: a minimax approach , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[9]  T. K. C. Peng,et al.  Adaptive Guaranteed Cost of Control of Systems with Uncertain Parameters , 1970 .

[10]  C.E. de Souza,et al.  Robust H/sub infinity / control for linear systems with norm-bounded time-varying uncertainty , 1990, 29th IEEE Conference on Decision and Control.

[11]  D. McFarlane,et al.  Optimal guaranteed cost control and filtering for uncertain linear systems , 1994, IEEE Trans. Autom. Control..

[12]  E. Boukas,et al.  Optimal guaranteed cost control of uncertain discrete time-delay systems , 2003 .

[13]  Qing-Long Han,et al.  Optimal guaranteed cost control of linear uncertain systems with input constraints , 2004, Fifth World Congress on Intelligent Control and Automation (IEEE Cat. No.04EX788).

[14]  Ian R. Petersen,et al.  An LMI approach to output-feedback-guaranteed cost control for uncertain time-delay systems , 2000 .

[15]  Eduardo F. Costa,et al.  On the design of guaranteed cost controllers for a class of uncertain linear systems , 2002, Syst. Control. Lett..