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Estimation of Null Controllable Region

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Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 193))

Abstract

In recent results on linear systems subject to actuator saturation, characterizations of null controllable regions form a guideline for searching feedback laws. Null controllable region , which is also called controllable set, is closely relative with time optimal control [25]. Null controllability of a control system is the possibility of steering its state to origin in finite time by an admissible control input [47]. A formula for extremes of the null controllable region of a discrete-time system with bounded inputs has been presented in [44]. An iterative approach for descriptions of the null controllable regions of continuous-time and traditional discrete-time systems with saturating inputs is found in [23] and [24], respectively. Null controllable problems on both continuous-time systems and traditional discrete-time systems subject to actuator saturation have been studied in [44] and [53], respectively. Some problems on the null controllable regions for systems with actuator saturation are important and challenging in both theory and practice, but the null controllable regions of DOSs with actuator saturation have not been proven yet, which motivated us to carry on this chapter.

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References

  1. S. Boyd, L. Vandenberghe, Convex Optimization (Cambridge University Press, Cambridge, 2004)

    Book  MATH  Google Scholar 

  2. M.L. Corradini, A. Cristofaro, F. Giannoni, Computation of null controllable regions for antistable linear systems subject to input saturation: an iterative approach. IET Control Theory Appl. 5(5), 744–749 (2011)

    Article  MathSciNet  Google Scholar 

  3. A. Cristofaro, M.L. Corradini, F. Giannoni, An iterative approach for the description of null controllable regions of discrete-time linear systems with saturating inputs, in Proceedings of the 19th Mediterranean Conference on Control and Automation, Greece, 2011, pp. 96–101

    Google Scholar 

  4. C.A. Desoer, J. Wing, An optimal strategy for a saturating sampled data system. IEEE Trans. Autom. Control 6(1), 5–15 (1961)

    Article  MathSciNet  Google Scholar 

  5. T. Hu, E.M. Daniel, L. Qiu, Null controllable region of LTI discrete-time systems with input saturation. Automatica 38(11), 2009–2013 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  6. T. Hu, Z. Lin, Control Systems with Actuator Saturation (Birkhäuser, Boston 2001)

    Book  MATH  Google Scholar 

  7. T. Hu, Z. Lin, L. Qiu, An explicit description of null controllable regions of linear systems with saturating actuators. Syst. Control Lett. 47(1), 65–78 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. J.L. LeMay, Recoverable and reachable zones for control systems with linear plants and bounded controller outputs. IEEE Trans. Autom. Control 4(9), 346–354 (1964)

    Article  MathSciNet  Google Scholar 

  9. H. Yang, Y. Xia, P. Shi, L. Zhao, Analysis and Synthesis of Delta Operator Systems (Springer, Berlin/Heidelberg, 2012)

    Book  Google Scholar 

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Yang, H., Xia, Y., Geng, Q. (2019). Estimation of Null Controllable Region . 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_2

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