Stabilisation of discrete-time bilinear systems by constant control inputs

References

• Amato F., Cosentino C., & Merola A. (2009). Stabilization of bilinear systems via linear state-feedback control. IEEE Transactions on Circuits and Systems II: Express Briefs, 56(1), 76–80. doi: 10.1109/TCSII.2008.2008528
   Web of Science ®Google Scholar
• Bose T., & Chen M. Q. (1995). BIBO stability of the discrete-time bilinear system. Digital Signal Processing, 5(3), 160–166. doi: 10.1006/dspr.1995.1016
   Web of Science ®Google Scholar
• Bruni C., Pillo G. D., & Koch G. (1974). Bilinear systems: An appealing class of ‘nearly linear’ systems in theory and applications. IEEE Transactions on Automatic Control, 19(4), 334–348. doi: 10.1109/TAC.1974.1100617
   Web of Science ®Google Scholar
• Chabour O., & Vivalda J. C. (2000). Remark on local and global stabilization of homogeneous bilinear systems. Systems & Control Letters, 41(2), 141–143. doi: 10.1016/S0167-6911(00)00045-1
   Web of Science ®Google Scholar
• Chen M. S., & Tsao S. T. (2000). Exponential stabilization of a class of unstable bilinear systems. IEEE Transactions on Automatic Control, 45(5), 989–992. doi: 10.1109/9.855570
   Web of Science ®Google Scholar
• Chiou J. S., Kung F. C., & Li T. H. S. (2000). Robust stabilization of a class of singularly perturbed discrete-time bilinear systems. IEEE Transactions on Automatic Control, 45(6), 1187–1191. doi: 10.1109/9.863604
   Web of Science ®Google Scholar
• Elliott D. L. (2009). Bilinear control systems: Matrices in action. Dordrecht: Springer.
   Google Scholar
• Fainshil L., & Margaliot M. (2012). A maximum principle for the stability analysis of positive bilinear control systems with applications to positive linear switched systems. SIAM Journal on Control and Optimization, 50(4), 2193–2215. doi: 10.1137/11083808X
   Web of Science ®Google Scholar
• Fliess M. (1981). Fonctionnelles causales non linéaires et indé terminées non commutatives. Bulletin de la Société Math ématique de France, 109(1), 3–40. doi: 10.24033/bsmf.1931
   Google Scholar
• Gounaridis-Minaidis C. H., & Kalouptsidis N. (1986). Stability of discrete-time bilinear systems with constant inputs. International Journal of Control, 43(2), 663–669. doi: 10.1080/00207178608933492
   Web of Science ®Google Scholar
• Hu B., Zhai G., & Michel A. N. (2012). Stabilization of two-dimensional single-input bilinear systems with a finite number of constant feedback controllers. Proceedings of the American control conference, Anchorage (pp. 1874–1879). IEEE.
   Google Scholar
• Hwang Y. R., Chen M. S., & Wu T. (2003). Division controllers for homogeneous dyadic bilinear systems. IEEE Transactions on Automatic Control, 48(4), 701–705. doi: 10.1109/TAC.2003.809773
   Web of Science ®Google Scholar
• Mohler R. R. (1973). Bilinear control processes. New York, NY: Academic.
   Google Scholar
• Mohler R. R. (1991). Nonlinear systems, vol. II, applications to bilinear control. Englewood Cliffs, NJ: Prentice-Hall.
   Google Scholar
• Mohler R. R., & Kolodziej W. J. (1980). An overview of bilinear systems theory and applications. IEEE Transactions on Systems, Man, and Cybernetics, 10(11), 683–688.
   Google Scholar
• Ogata K. (1995). Discrete-time control systems. Englewood Cliffs, NJ: Prentice-Hall.
   Google Scholar
• Omran H., Hetel L., Richard J. P., & Lamnabhi F. (2014). Stability analysis of bilinear systems under aperiodic sampled-data control. Automatica, 50(4), 1288–1295. doi: 10.1016/j.automatica.2014.02.033
   Web of Science ®Google Scholar
• Ouzahra M. (2009). Stabilisation of infinite-dimensional bilinear systems using a quadratic feedback control. International Journal of Control, 82(9), 1657–1664. doi: 10.1080/00207170802657348
   Web of Science ®Google Scholar
• Tie L. (2013). On stabilization of continuous-time and discrete-time symmetric bilinear systems by constant controls. 9th Asian control conference, Istanbul (pp. 1–6). IEEE.
   Google Scholar
• Tie L. (2014). On near-controllability, nearly-controllable subspaces, and near-controllability index of a class of discrete-time bilinear systems: A root locus approach. SIAM Journal on Control and Optimization, 52(2), 1142–1165. doi: 10.1137/120892878
   Web of Science ®Google Scholar
• Tie L. (2016). On controllability of discrete-time bilinear systems by near-controllability. Systems & Control Letters, 98(5), 14–24. doi: 10.1016/j.sysconle.2016.09.019
   Google Scholar
• Tie L. (2017). On controllability of homogeneous and inhomogeneous discrete-time multi-input bilinear systems in dimension two. International Journal of Control, 90(9), 1752–1768. doi: 10.1080/00207179.2016.1221137
   Google Scholar
• Yang X., Chen L. K., & Burton R. M. (1989). Stability of discrete-time bilinear systems with output feedback. International Journal of Control, 50(5), 2085–2092. doi: 10.1080/00207178908953483
   Web of Science ®Google Scholar