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

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Abstract

Estimation of the DoA is a key of control systems with actuator saturation which is applicable to various literatures [2, 26]. Ellipsoids are usually used as a shape of the DoA [93, 145]. Researches on the DoA have been given for uncertain polynomial continuous-time systems in [19]. Analytical approximation of a maximal invariant ellipsoid has been discussed for discrete-time systems with bounded controls [199]. The DoA has been given for linear time-invariant systems subject to disturbances and state constraints [133]. Monotonicity of a maximal invariant ellipsoid has been analyzed for a linear system with actuator saturation [197].

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References

  1. F. Amato, R. Ambrosino, M. Ariola, A. Merola, Domain of attraction and guaranteed cost control for non-linear quadratic systems. Part 2: controller design. IET Control Theory Appl. 7(4), 565–572 (2013)

    Google Scholar 

  2. G. Chesi, Rational Lyapunov functions for estimating and controlling the robust domain of attraction. Automatica 49(4), 1051–1057 (2013)

    Article  MathSciNet  Google Scholar 

  3. H. Dong, Y. Joo, M. Tak, Linear matrix inequality approach to local stability analysis of discrete-time Takagic–Sugeno fuzzy systems. IET Control Theory Appl. 7(9), 1309–1318 (2013)

    Article  MathSciNet  Google Scholar 

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

    Book  Google Scholar 

  5. T. Kailath, Linear Systems (Prentice-Hall, Inc Press, Englewood Cliffs, 1980)

    Google Scholar 

  6. J. Luo, J. Zhao, Robust control for a class of uncertain switched fuzzy systems with saturating actuators. Asian J. Control 17(4), 1462–1469 (2015)

    Article  MathSciNet  Google Scholar 

  7. T. Thibodeau, W. Tong, T. Hu, Set invariant and performance analysis of linear systems via truncated ellipsoids. Automatica 45(9), 2046–2051 (2009)

    Article  MathSciNet  Google Scholar 

  8. Y. Wu, H. Su, Z. Wu, Synchronisation control of dynamical networks subject to variable sampling and actuators saturation. IET Control Theory Appl. 9(3), 381–391 (2015)

    Article  MathSciNet  Google Scholar 

  9. B. Zhou, G. Duan, On analyitical of the maximal invariant ellipsoid for linear systems with bounded control. IEEE Trans. Autom. Control 54(2), 346–353 (2009)

    Article  Google Scholar 

  10. B. Zhou, G. Duan, Z. Lin, Approximation and monotonicity of the maximal invariant ellipsoid for discrete-time systems by bounded controls. IEEE Trans. Autom. Control 55(2), 440–446 (2010)

    Article  MathSciNet  Google Scholar 

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Yang, H., Xia, Y., Geng, Q. (2019). Monotonicity and Parametric Riccati Equation. 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_9

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