Abstract
The stability investigation of 2-D discrete systems has been one of the most explored areas for the researchers due to its wide variety of practical and diversified applications. The 2-D discrete systems stability analysis using \( H_{\infty } \) control technique has always been an active field of research. The \( H_{\infty } \) control techniques play a vital role in the analysis and design work of control and signal processing systems. A detailed survey report of 2-D discrete systems has been presented on the stability analysis using \( H_{\infty } \) control techniques.
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References
Shaked, U., Theodor, Y.: H∞-optimal estimation: a tutorial. In: 31st Conference on Decision Control, pp. 2278–2286 (1992)
Zames, G.: Feedback and optimal sensitivity: model reference transformations, multiplicative seminorms, and approximate inverses. IEEE Trans. Automat. Contr. 26(2), 301–320 (1981)
Xie, L., Soh, Y.C., de Souza, C.E.: Robust Kalman filtering for uncertain discrete-time systems. IEEE Trans. Automat. Control 39, 1310–1314 (1994)
Glover, K.: All optimal Hankel-norm approximations of linear multivariable systems and their L∞ error bounds. Int. J. Contr. 39, 1115–1193 (1984)
Ball, J.A., Cohen, N.: Sensitivity minimization in an H∞ norm: parametrization of all sub-optimal solutions. Int. J. Contr. 46, 785–816 (1987)
Boyd, S., Balakrishnan, V., Kabamba, P.: On computing the H∞ norm of a transfer matrix. Math. Contr. Signals, Syst. (1998)
Doyle, J.C.: Lecture Notes in Advances in Multivariable Control: ONR/Honeywell Workshop. Minneapolis, MN (1984)
Zhou, K., Doyle, J.C., Keith, G.: Robust and Optimal Control. Prentice-Hall, NJ (1996)
Glover, K., Doyle, J.C.: A state space approach to H∞ optimal control. Three Decad. Math. Syst. Theory 135(1), 179–218 (1989)
Kabamba, P.T., Boyd, S.P.: On parametric H∞ optimization. In: Proceedings of the 27th Conference on Decision and Control, Austin, Texas, pp. 1354–1355 (1988)
Francis, B.A., Helton, J.W., Zames, G.: H∞ optimal feedback controllers for linear multivariable systems. IEEE Trans. Automat. Contr. 29(10), 888–900 (1984)
Zhou, K., Doyle, J.C., Glover, K.: Robust and Optimal Control. Prentice-Hall, NJ (1996)
Khargonekar, P.P., Rotea, M.A.: Mixed H2/H∞ control: a convex optimization approach. IEEE Trans. Automat. Contr. 36(7), 824–837 (1991)
Khargonekar, P.P., Petersen, I.R., Zhou, K.: Robust stabilization of uncertain linear systems: quadratic stabilizability and H∞ control theory. IEEE Trans. Automat. Contr. 35(3), 356–361 (1990)
Du, C., Xie, L.: H∞ Control and Filtering of Two-Dimensional Systems, vol. 278. Lecture Notes in Control and Information Sciences. Springer, Berlin (2002)
Galkowski, K.: State-Space Realisation of Linear 2-D Systems with Extensions to the General n D case, vol. 263. Lecture Notes in Control and Information Sciences. Springer, London (2001)
Sebek, M.: H∞ problem of 2-D systems. In: Proceeding of the European Control Conference, Groningen, Netherlands, pp. 1476–1479 (1993)
Du, C., Xie, L., Soh, Y.C.: H∞ filtering of 2-D discrete systems. IEEE Trans. Signal Process. 48, 1760–1768 (2000)
Petersen, I.: Disturbance attenuation and H∞ optimization: a design method based on the algebraic Riccati equation. IEEE Trans. Automat. Contr. 32(5), 427–429 (1987)
Cao, J., Sivasamy, R., Rakkiyappan, R.: Sampled data H∞ synchronization of chaotic Lur’e systems with Time delay. Circuits, Syst. Signal Process. 35(3), 811–835 (2016)
Cao, J., Rakkiyappan, R., Maheswari, K., Chandrasekar, A.: Exponential H∞ filtering analysis for discrete time switched neural networks with random delays using sojourn probabilities. Sci. China Technol. Sci. 59(3), 387–402 (2016)
De Souza, C.E., Fu, M., Xie, L.: H∞ analysis and synthesis of discrete-time systems with time-varying uncertainty. IEEE Trans. Automat. Control 38, 459–462 (1993)
Dharani, S., Rakkiyappan, R., Cao, J.: Robust stochastic sampled data H∞ control for a class of mechanical systems with uncertainties. ASME J. Dyn. Syst., Meas. Control. 137(10), 1–14 (2015)
Du, C., Xie, L., Zhang, C.: H∞ control and robust stabilization of two-dimensional systems in Roesser models. Automatica 37, 205–211 (2001)
Farges, C., Peaucelle, D., Arzelier, D., Daafouz, J.: Robust H∞ performance analysis and synthesis of linear polytopic discrete-time periodic systems via LMIs. Syst. Control. Lett. 56, 159–166 (2007)
Francis, B.A., Doyle, J.C.: Linear control theory with an H∞ optimality criterion. SIAM J. Control Optim. 25(4), 815–844 (1987)
Gao, H., Lam, J., Xu, S., Wang, C.: Stabilization and H∞ control of two dimensional Markovian jump systems. IMA J. Math. Control. Inf. 21, 377–392 (2004)
Khargonekar, P.P., Petersen, I.R., Rotea, M.A.: H∞ optimal control with state-feedback. IEEE Trans. Automat. Contr. 33(8), 786–788 (1988)
Paszke, W., Galkowski, K., Rogers, E., Owens, D.H.: H∞ and guaranteed cost control of discrete linear repetitive processes. Linear Algebr. Appl. 412, 93–131 (2006)
Xie, L., Du, C., Soh, Y.C., Zhang, C.: H∞ and robust control of 2-D systems in FM second model. Multidimens. Syst. Signal Process. 13(3), 265–287 (2002)
Feng, Z.Y., Xu, L., Anazawa, Y.: Sufficient LMI conditions for H∞ static output feedback control of 2-D systems. In: 11th International Conference on Control, Automation, Robotics and Vision. Singapore, pp. 57–60 (2010)
Feng, Z.Y., Xu, L., Wu, M., She, J.H.: H∞ static output feedback control of 2-D discrete systems in FM second model. Asian J. Control 14(6), 1505–1513 (2012)
Xie, L., Du, C., Zhang, C., Soh, Y.C.: H∞ deconvolution filtering of 2-D digital systems. IEEE Trans. Signal Process. 50, 2319–2331 (2002)
Xu, H., Zou, Y., Xu, S., Guo, L.: Robust H∞ control for uncertain two-dimensional discrete systems described by the general model via output feedback controllers. Int. J. Contr. Automation Syst. 6(5), 785–791 (2008)
Yang, R., Xie, L., Zhang, C.: H2 and mixed H2/H∞ control of two-dimensional systems in Roesser model. Automatica 42(9), 1507–1514 (2006)
Xu, J., Yu, L.: H∞ control of 2-D discrete state delay systems. Int. J. Control., Autom. Syst. 4, 516–523 (2006)
Xu, J., Yu, L.: H∞ control for 2-D discrete state delayed systems in the second FM model. Acta Automatica Sinicia 34, 809–813 (2008)
Xu, J., Yu, L.: Delay-dependent H∞ control for 2-D discrete state delay systems in the second FM model. Multidim. Syst. Sig. Process. 20, 333–349 (2009)
Lu, W.S., Luo, H., Antoniou, A.: Recent results on model reduction methods for 2-D discrete systems and Systems. In: ISCAS, pp. 348–351 (1996)
Luo, H., Lu, W.S., Antoniou, A.: A weighted balanced approximation for 2-D discrete systems and its application to model reduction. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 42(8), 419–429 (1995)
Zhou, K., Aravena, J.L., Gu, G., Xiong, D.: 2-D model reduction by quasi-balanced truncation and singular perturbation. IEEE Trans. Circuits Syst. II Analog Digit. Signal Process. 41(9), 593–602 (1994)
Duan, Z., Xiang, Z.: State feedback H∞ control for discrete 2-D switched systems. J. Franklin Institute. 350, 1513–1530 (2013)
Crusius, C.A.R., Trofino, A.: Sufficient LMI conditions for output feedback control problems. IEEE Trans. Automat. Control 44, 1053–1057 (1999)
Lee, K.H., Lee, J.H., Kwon, W.H.: Sufficient LMI conditions for H∞ output feedback stabilization of linear discrete-time systems. 51(4), 675–680 (2006)
Yu, L., Gao, F.: Output feedback guaranteed cost control for uncertain discrete-time systems using linear matrix inequalities. J. Optim. Theory Appl., 113, 621–634 (2002)
Lu, W.S.: On a Lyapunov approach to stability analysis of 2-D digital filters. IEEE Trans. Circuits Syst. I 41, 665–669 (1994)
Ahn, C.K.: \( l_{\,2} - l_{\,\infty } \) Elimination of overflow oscillations in 2-D digital filters described by the Roesser model with external interference. IEEE Trans. Circuits Syst II. 60(6), 361–365 (2013)
Doyle, J.C., Glover, K., Khargonekar, P.P., Francis, B.A.: State space solutions to standard H2 and H∞ control problems. IEEE Trans. Automat. Contr. 34(8), 831–847 (1989)
Hassibi, B., Sayed, A.H., Kailath, T.: Indefinite Quadratic Estimation and Control a Unified Approach to H2/H∞ Theories. Siam, Philadelphia (1999)
Francis, B.A.: A Course in H∞ Control Theory. Lecture Notes in Control and Information Sciences. Springer, London (1987)
Glover, K., Doyle, J.C.: State-space formulae for all stabilizing controllers that satisfy an H∞-norm bound and relations to risk sensitivity. Syst. Control Lett. 11(3), 167–172 (1988)
Doyle, J.C.: Guaranteed margins for LQG regulators. IEEE Trans. Automat. Control 26(4), 756–757 (1978)
He, Y., Wu, M., She, J.H.: Improved bounded-real lemma representation and H∞ control of systems with polytopic uncertainties. IEEE Trans. Circuits Syst. II 52, 380–383 (2005)
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Vidyarthi, A., Tiwari, M. (2020). A Survey on \( H_{\infty } \) Control Techniques. In: Dutta, D., Kar, H., Kumar, C., Bhadauria, V. (eds) Advances in VLSI, Communication, and Signal Processing. Lecture Notes in Electrical Engineering, vol 587. Springer, Singapore. https://doi.org/10.1007/978-981-32-9775-3_72
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DOI: https://doi.org/10.1007/978-981-32-9775-3_72
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