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Języki publikacji
Abstrakty
This investigation is concerned with robust analysis and control of uncertain nonlinear systems with parametric uncertainties. In contrast to the methodologies from the field of linear parameter varying systems, which employ convex structures of the state space representation in order to perform analysis and design, the proposed approach makes use of a polytopic form of a generalisation of the characteristic polynomial, which proves to outperform former results on the subject. Moreover, the derived conditions have the advantage of being cast as linear matrix inequalities under mild assumptions.
Rocznik
Tom
Strony
275--283
Opis fizyczny
Bibliogr. 36 poz., wykr.
Twórcy
autor
- Department of Electric and Electronics Engineering, Sonora Institute of Technology, 5 de Febrero 818 Sur, CP 85000, Ciudad Obregon, Sonora, Mexico
autor
- Department of Electric and Electronics Engineering, Sonora Institute of Technology, 5 de Febrero 818 Sur, CP 85000, Ciudad Obregon, Sonora, Mexico
Bibliografia
- [1] Amato, F., Pironti, A. and Scala, S. (1996). Necessary and sufficient conditions for quadratic stability and stabilizability of uncertain linear time-varying systems, IEEE Transactions on Automatic Control 41(1): 125–128.
- [2] Apkarian, P. and Gahinet, P. (1995). A convex characterization of gain-scheduled h∞ controllers, IEEE Transactions on Automatic Control 40(5): 853–864.
- [3] Barber, C.B., Dobkin, D.P. and Huhdanpaa, H. (1996). The quickhull algorithm for convex hulls, ACM Transactions on Mathematical Software (TOMS) 22(4): 469–483.
- [4] Barmish, B.R., Hollot, C.V., Kraus, F.J. and Tempo, R. (1992). Extreme point results for robust stabilization of interval plants with first-order compensators, IEEE Transactions on Automatic Control 37(6): 707–714.
- [5] Bartlett, A.C., Hollot, C.V. and Lin, H. (1988). Root locations of an entire polytope of polynomials: It suffices to check the edges, Mathematics of Control, Signals and Systems 1(1): 61–71.
- [6] Baumann, W. and Rugh, W. (1986). Feedback control of nonlinear systems by extended linearization, IEEE Transactions on Automatic Control 31(1): 40–46.
- [7] Białas, S. (1985). A necessary and sufficient condition for the stability of convex combinations of stable polynomials or matrices, Bulletin of the Polish Academy of Sciences 33(9–10): 473–480.
- [8] Białas, S. and Góra, M. (2012). A few results concerning the Hurwitz stability of polytopes of complex polynomials, Linear Algebra and Its Applications 436(5): 1177–1188.
- [9] Boyd, S., Ghaoui, L.E., Feron, E. and Belakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA.
- [10] Dorf, R. and Bishop, R. (1998). Modern Control Systems, Pearson (Addison-Wesley), Upper Saddle River, NJ.
- [11] Ebihara, Y., Peaucelle, D., Arzelier, D., Hagiwara, T. and Oishi, Y. (2012). Dual LMI approach to linear positive system analysis, 12th International Conference on Control, Automation and Systems (ICCAS), JeJu Island, South Korea, pp. 887–891.
- [12] Gahinet, P., Nemirovski, A., Laub, A.J. and Chilali, M. (1995). LMI Control Toolbox, Math Works, Natick, MA.
- [13] Gonzláez, T. and Bernal, M. (2016). Progressively better estimates of the domain of attraction for nonlinear systems via piecewise Takagi–Sugeno models: Stability and stabilization issues, Fuzzy Sets and Systems 297: 73–95.
- [14] Gonzláez, T., Bernal, M., Sala, A. and Aguiar, B. (2017). Cancellation-based nonquadratic controller design for nonlinear systems via Takagi–Sugeno models, IEEE Transactions on Cybernetics 47(9): 2628–2638.
- [15] Guerra, T.M., Estrada-Manzo, V. and Lendek, Z. (2015). Observer design of nonlinear descriptor systems: An LMI approach, Automatica 52: 154–159.
- [16] Guerra, T.M. and Vermeiren, L. (2004). LMI-based relaxed non-quadratic stabilization conditions for nonlinear systems in Takagi–Sugeno’s form, Automatica 40(5): 823–829.
- [17] Henrion, D., Sebek, M. and Kucera, V. (2003). Positive polynomials and robust stabilization with fixed-order controllers, IEEE Transactions on Automatic Control 48(7): 1178–1186.
- [18] Johansen, T.A. (2000). Computation of Lyapunov functions for smooth nonlinear systems using convex optimization, Automatica 36(11): 1617–1626.
- [19] Khalil, H. (2002). Nonlinear Systems, 3rd Edn., Prentice Hall, Upper Saddle River, NJ.
- [20] Kharitonov, V. (1978). Asymptotic stability of an equilibrium position of a family of systems of linear differential equations, Differential Equations 14(11): 1483–1485.
- [21] Kwiatkowski, A., Boll, M. and Werner, H. (2006). Automated generation and assessment of affine LPV models, 45th IEEE Conference on Decision and Control, San Diego, CA, USA, pp. 6690–6695.
- [22] Pan, J., Guerra, T., Fei, S. and Jaadari, A. (2012). Nonquadratic stabilization of continuous T–S fuzzy models: LMI solution for a local approach, IEEE Transactions on Fuzzy Systems 20(3): 594–602.
- [23] Rhee, B. and Won, S. (2006). A new fuzzy Lyapunov function approach for a Takagi–Sugeno fuzzy control system design, Fuzzy Sets and Systems 157(9): 1211–1228.
- [24] Robles, R., Sala, A., Bernal, M. and Gonzláez, T. (2017). Subspace-based Takagi–Sugeno modeling for improved LMI performance, IEEE Transactions on Fuzzy Systems 25(4): 754–767.
- [25] Sala, A. and Ario, C. (2009). Polynomial fuzzy models for nonlinear control: A Taylor series approach, IEEE Transactions on Fuzzy Systems 17(6): 1284–1295.
- [26] Sala, A. and Ariño, C. (2007). Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Applications of Polya’s theorem, Fuzzy Sets and Systems 158(24): 2671–2686.
- [27] Sanchez, M. and Bernal, M. (2017). A convex approach for reducing conservativeness of Kharitonov’s-based robustness analysis, 20th IFAC World Congress, Toulouse, France, pp. 855–860.
- [28] Shamma, J.S. and Cloutier, J.R. (1992). A linear parameter varying approach to gain scheduled missile autopilot design, American Control Conference, Chicago, IL, USA, pp. 1317–1321.
- [29] Sideris, A. and Barmish, B.R. (1989). An edge theorem for polytopes of polynomials which can drop in degree, Systems & Control Letters 13(3): 233–238.
- [30] Sturm, J.F. (1999). Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones, Optimization Methods and Software 11(1–4): 625–653.
- [31] Tanaka, K., Hori, T. and Wang, H. (2003). A multiple Lyapunov function approach to stabilization of fuzzy control systems, IEEE Transactions on Fuzzy Systems 11(4): 582–589.
- [32] Tanaka, K. and Wang, H. (2001). Fuzzy Control Systems Design and Analysis. A Linear Matrix Inequality Approach, John Wiley&Sons, New York, NY.
- [33] Taniguchi, T., Tanaka, K. and Wang, H. (2001). Model construction, rule reduction and robust compensation for generalized form of Takagi–Sugeno fuzzy systems, IEEE Transactions on Fuzzy Systems 9(2): 525–537.
- [34] Tapia, A., Bernal, M. and Fridman, L. (2017). Nonlinear sliding mode control design: An LMI approach, Systems & Control Letters 104: 38–44.
- [35] Wang, H., Tanaka, K. and Griffin, M. (1996). An approach to fuzzy control of nonlinear systems: Stability and design issues, IEEE Transactions on Fuzzy Systems 4(1): 14–23.
- [36] Xu, S., Darouach, M. and Schaefers, J. (1993). Expansion of det(a + b) and robustness analysis of uncertain state space systems, IEEE Transactions on Automatic Control 38(11): 1671–1675.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-6d339f97-6d00-4e8e-bc30-3fbb4f7a082d