References
- 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 Control41(1): 125–128.
- Apkarian, P. and Gahinet, P. (1995). A convex characterization of gain-scheduled h∞ controllers, IEEE Transactions on Automatic Control40(5): 853–864.
- 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.
- 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 Control37(6): 707–714.
- 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 Systems1(1): 61–71.
- Baumann, W. and Rugh, W. (1986). Feedback control of nonlinear systems by extended linearization, IEEE Transactions on Automatic Control31(1): 40–46.
- 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 Sciences33(9–10): 473–480.
- Białas, S. and Góra, M. (2012). A few results concerning the Hurwitz stability of polytopes of complex polynomials, Linear Algebra and Its Applications436(5): 1177–1188.
- Boyd, S., Ghaoui, L.E., Feron, E. and Belakrishnan, V. (1994). Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA.
- Dorf, R. and Bishop, R. (1998). Modern Control Systems, Pearson (Addison-Wesley), Upper Saddle River, NJ.
- 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.
- Gahinet, P., Nemirovski, A., Laub, A.J. and Chilali, M. (1995). LMI Control Toolbox, Math Works, Natick, MA.
- González, 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 Systems297: 73–95.
- González, T., Bernal, M., Sala, A. and Aguiar, B. (2017). Cancellation-based nonquadratic controller design for nonlinear systems via Takagi–Sugeno models, IEEE Transactions on Cybernetics47(9): 2628–2638.
- Guerra, T.M., Estrada-Manzo, V. and Lendek, Z. (2015). Observer design of nonlinear descriptor systems: An LMI approach, Automatica52: 154–159.
- Guerra, T.M. and Vermeiren, L. (2004). LMI-based relaxed non-quadratic stabilization conditions for nonlinear systems in Takagi–Sugeno’s form, Automatica40(5): 823–829.
- Henrion, D., Sebek, M. and Kucera, V. (2003). Positive polynomials and robust stabilization with fixed-order controllers, IEEE Transactions on Automatic Control48(7): 1178–1186.
- Johansen, T.A. (2000). Computation of Lyapunov functions for smooth nonlinear systems using convex optimization, Automatica36(11): 1617–1626.
- Khalil, H. (2002). Nonlinear Systems, 3rd Edn., Prentice Hall, Upper Saddle River, NJ.
- Kharitonov, V. (1978). Asymptotic stability of an equilibrium position of a family of systems of linear differential equations, Differential Equations14(11): 1483–1485.
- 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.
- 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 Systems20(3): 594–602.
- Rhee, B. and Won, S. (2006). A new fuzzy Lyapunov function approach for a Takagi–Sugeno fuzzy control system design, Fuzzy Sets and Systems157(9): 1211–1228.
- Robles, R., Sala, A., Bernal, M. and González, T. (2017). Subspace-based Takagi–Sugeno modeling for improved LMI performance, IEEE Transactions on Fuzzy Systems25(4): 754–767.
- Sala, A. and Ario, C. (2009). Polynomial fuzzy models for nonlinear control: A Taylor series approach, IEEE Transactions on Fuzzy Systems17(6): 1284–1295.
- 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 Systems158(24): 2671–2686.
- 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.
- 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.
- Sideris, A. and Barmish, B.R. (1989). An edge theorem for polytopes of polynomials which can drop in degree, Systems & Control Letters13(3): 233–238.
- Sturm, J.F. (1999). Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones, Optimization Methods and Software11(1–4): 625–653.
- Tanaka, K., Hori, T. and Wang, H. (2003). A multiple Lyapunov function approach to stabilization of fuzzy control systems, IEEE Transactions on Fuzzy Systems11(4): 582–589.
- Tanaka, K. and Wang, H. (2001). Fuzzy Control Systems Design and Analysis. A Linear Matrix Inequality Approach, John Wiley&Sons, New York, NY.
- 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 Systems9(2): 525–537.
- Tapia, A., Bernal, M. and Fridman, L. (2017). Nonlinear sliding mode control design: An LMI approach, Systems & Control Letters104: 38–44.
- Wang, H., Tanaka, K. and Griffin, M. (1996). An approach to fuzzy control of nonlinear systems: Stability and design issues, IEEE Transactions on Fuzzy Systems4(1): 14–23.
- 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 Control38(11): 1671–1675.