Abstract
Using traditional methods on LMIs , an invariant set Ω(P, ρ) as the DoA has been obtained in [52]. All trajectories of a control system are kept inside the DoA at every step [163]. An important issue of the works in previous chapters is how to design a proper controller and how to estimate the DoA for DOSs with actuator saturation . Note that invariant ellipsoids are also used to estimate the DoA of DOSs [45]. In [19], researches on the DoA have been given for uncertain polynomial continuous-time systems . Moreover, a central idea of existing methodologies on estimating the DoA is to use a contractively invariant set associated to proper Lyapunov functions , such as Lyapunov functions with ellipsoidal estimates, polyhedral Lyapunov functions , and piecewise quadratic Lyapunov functions . Although these problems have been examined extensively from various aspects recently, estimating and enlarging the DoA is still a difficult task.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
G. Chesi, Rational Lyapunov functions for estimating and controlling the robust domain of attraction. Automatica 49(4), 1051–1057 (2013)
T. Hu, B. Huang, Z. Lin, Absolute stability with a generalized sector condition. IEEE Trans. Autom. Control 49(4), 535–548 (2004)
T. Hu, Z. Lin, On enlarging the basin of attraction for linear systems under saturated linear feedback. Syst. Control Lett. 40(1), 59–69 (2000)
T. Hu, Z. Lin, Control Systems with Actuator Saturation (Birkhäuser, Boston 2001)
T. Hu, Z. Lin, B.M. Chen, An analysis and design method for linear systems subject to actuator saturation and disturbances. Automatica 38(2), 351–359 (2002)
H. Yang, P. Shi, Z. Li, C. Hua, Analysis and design for delta operator systems with actuator saturation. Int. J. Control 87(5), 987–999 (2014)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Yang, H., Xia, Y., Geng, Q. (2019). A Lifting Technique for Sampling Periods . In: Analysis and Synthesis of Delta Operator Systems with Actuator Saturation. Studies in Systems, Decision and Control, vol 193. Springer, Singapore. https://doi.org/10.1007/978-981-13-3660-7_6
Download citation
DOI: https://doi.org/10.1007/978-981-13-3660-7_6
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-3659-1
Online ISBN: 978-981-13-3660-7
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)