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descriptor system; robust PI-D controller; state derivative feedback; output feedback; pole placement
The paper deals with the problem of obtaining a robust PI-D controller design procedure for linear time invariant descriptor uncertain polytopic systems using the regional pole placement and/or $H_2$ criterion approach in the form of a quadratic cost function with the state, derivative state and plant input (QSR). In the frame of Lyapunov Linear Matrix Inequality (LMI) regional pole placement approach and/or $H_2$ quadratic cost function based on Bellman-Lyapunov equation, the designed novel design procedure guarantees the robust properties of closed-loop system with parameter dependent quadratic stability/quadratic stability. In the obtained design procedure the designer could use controller with different structures such as P, PI, PID, PI-D. For the PI-D's D-part of controller feedback the designer could choose any available output/state derivative variables of descriptor systems. Obtained design procedure is in the form of Bilinear Matrix Inequality (BMI). The effectiveness of the obtained results is demonstrated on two examples.
[1] Bara, G. J.: Robust analysis and control of parameter-dependent uncertaintain descriptor systems. Systems Control Lett. 60 (2011), 356-364. DOI 10.1016/j.sysconle.2011.03.001 | MR 2838901
[2] Darouch, M., Ameto, F., Alma, M.: Functional observers design for descriptor systems via LMI: Continuous and Discrete-time cases. Automatika 86 (2017), 216-219. DOI 10.1016/j.automatica.2017.08.016 | MR 3711466
[3] Debeljkovic, D., Visnjic, N., Pjescic, M.: The stability of linear continuous singular systems in the sense of Lyapunov: An overview. Sci. Techn. Rev. LVII (2007), 1, 51-64. MR 2483390
[4] Fu, M.: Pole Placement via static output feedback is NP-hard. IEEE Trans Automat. Control 49 (2004), 5, 855-857. DOI 10.1109/tac.2004.828311 | MR 2057831
[5] Hien, L. Van, Vu, L. H., Trinh, H.: Stability of two dimmensional descriptor systems with generalized directional delays. Systems Control Lett. 112 (2018), 42-50. DOI 10.1016/j.sysconle.2017.12.003 | MR 3763875
[6] Chadli, M., Daafouz, J., Darouch, M.: Stabilization of Singular LPV systems. In: Proc. of 17th IFAC World Congress 2008, pp. 9999-10002. DOI 10.3182/20080706-5-kr-1001.01692
[7] Chen, C., Liu, Y.: Lyapunov stability analysis of linear singular dynamical systems. In: Proc. Inter. Conf. on Intelligent Processing Systems, Beijing, 1997. DOI 10.1109/icips.1997.672862
[8] Chilali, M., Gahinet, P.: $H_{\infty}$ design with pole placement constraints: LMI approach. IEEE Trans. Automat. Control 41, 1996, 3, 358-365. DOI 10.1109/9.486637 | MR 1382985
[9] Chilali, M., Gahinet, P., Apkarian, P.: Robust pole placement in LMI regions. IEEE Trans. Automat. Control 44 (1999), 12, 2257-2269. DOI 10.1109/9.811208 | MR 1728961
[10] Ji, X., Su, H., Chu, J.: An LMI approach to robust $H_{\infty}$ control for uncertain singular time-delay systems. J. Control Theory Appl. 4 (2006), 361-366. DOI 10.1007/s11768-006-5212-2 | MR 2290104
[11] Kimura, H.: A futher result on the problem of pole assignment by output feedback. IEEE Trans. Automa. Control 22 (1977), 3, 458-467. DOI 10.1109/tac.1977.1101520 | MR 0465326
[12] Krokavec, D., Filasova, A.: LMI constraints on system eigenvalues placement in dynamic output control design. IEEE Conference on Control Appllications, 2015. DOI 10.1109/cca.2015.7320862
[13] Kucera, V., Souza, C. E.: A necessary and sufficient condition for output feedback stabilizability. Automatika 31 (1995), 9, 1357-1359. DOI 10.1016/0005-1098(95)00048-2 | MR 1349414
[14] Kuncevic, V. M., Lycak, M. M.: Control Systems Design Using Lyapunov Function Approach (In Russian). Nauka, Moscow 1977.
[15] Lin, Ch., Chen, B., Shi, P., Yu, J. P.: Necessary and sufficient conditions of observer-based stabilization for a class of fractional-order descriptor systems. Systems Control Lett. 112 (2018), 31-35. DOI 10.1016/j.sysconle.2017.12.004 | MR 3763873
[16] Lin, Ch., Wang, J. L., Yang, G. H., Soh, C. B.: Robust C-controllability and/or C-observability for uncertain desriptor systems with interval perturbations in all matrices. Trans. Automat. Control 44 (1999), 9, 1768-1773. DOI 10.1109/9.788550 | MR 1710126
[17] Masabuchi, I., Kamitane, Y., Ohara, A., Suda, N.: $H_{\infty}$ control for descriptive systems: A matrix inequalities approach. Automatika 33 (1997), 4, 669-673. DOI 10.1016/s0005-1098(96)00193-8 | MR 1448959
[18] Peaucelle, D., Arzelier, D., Bachelier, D., Bernussou, J.: A new robust D-stability condition for real convex polytopic uncertainty. Systems Control Lett. 40 (2000), 21-30. DOI 10.1016/s0167-6911(99)00119-x | MR 1829071 | Zbl 0977.93067
[19] Silva, M. S., deLima, T. P.: Looking for nonnegative solutions of a Leontiev dynamic model. Linear Algebra 364 (2003), 281-316. DOI 10.1016/s0024-3795(02)00569-4 | MR 1971101
[20] Takaba, K., Moriharu, N., Katayama, T.: A generalized Lyapunov Theorem for descriptive system. Systems Control Lett. 24 (1995), 49-51. DOI 10.1016/0167-6911(94)00041-s | MR 1307127
[21] Veselý, V., Körösi, L.: Robust PI-D controller design for uncertain linear polytopic systems using LMI regions and $H_2$ performance. IEEE Trans. Industry Appl. 55 (2019), 5, 5353-5359. DOI 10.1109/tia.2019.2921282
[22] Veselý, V., Rosinová, D.: Robust PID-PSD controller design: BMI approach. Asian J. Control 5 (2013), 2, 469-478. DOI 10.1002/asjc.559 | MR 3043456
[23] Xu, S., Dooren, P. Van, Stefan, R., Lam, J.: Robust stability and stabilization for singular systems with state delay and parameter uncertainty. IEEE Trans. Automat. Control (2002), 1-12. DOI 10.1109/tac.2002.800651 | MR 1911484
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