Positive real control of two-dimensional systems: Roesser models and linear repetitive processes

References

• Agathoklis, P., 1988, Lower bounds for the stability margin of discrete two-dimensional systems based on the two-dimensional Lyapunov equation. IEEE Transactions on Circuits Systems, 35, 745–749.
   Google Scholar
• Agathoklis, P., Jury, E. I., and Mansour, M., 1991, The importance of bounded real and positive real functions in the stability analysis of 2-D system. Proceedings of the IEEE Symposium on Circuits and Systems, pp. 124–127.
   Google Scholar
• Amman, N., Owens, D., and Rogers, E., 1998, Predictive optimal iterative learning control. International Journal of Control, 69, 203–226.
   Google Scholar
• Anderson, B. D. O., Agathoklis, P., Jury, E. I., and Mansour, M., 1986, Stability and the matrix Lyapunov equation for discrete 2-dimensional systems. IEEE Transactions on Circuits Systems, 33, 261–267.
   Google Scholar
• Anderson, B. D. O., and Vongpanitlerd, S., 1973, Network Analysis and Synthesis: A Modem Systems Theory Approach (Upper Saddle River, NJ: Prentice-Hall).
   Google Scholar
• Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V., 1994, Linear Matrix Inequalities in Systems and Control Theory, SIAM Studies in Applied Mathematics, Philadelphia, PA, USA.
   Google Scholar
• Edwards, J. B., 1974, Stability problems in the control of multipass processes. Proceedings of the Institution of Electrical Engineers, 12, 1425–1431.
   Google Scholar
• Fornasini, E., and Marchesini, G., 1976, State-space realization theory of two-dimensional filters. IEEE Transactions on Automatic Control, 21, 484–492.
   Google Scholar
• Fornasini, E., and Marchesini, G., 1978, Doubly-indexed dynamical systems: state space models and structural properties. Mathematical Systems Theory, 12, 59–72.
   Google Scholar
• Gahinet, P., and Apkarian, P., 1994, A linear matrix inequality approach to H∞ control. International Journal of Robust and Nonlinear Control, 4, 421–448.
   Google Scholar
• Galkowski, K., Rogers, E., and Owens, D., 1998, Matrix rank based conditions for reachability /controllability of discrete linear repetitive processes. Linear Algebra and its Applications, 275–276, 201–224.
   Google Scholar
• Haddad, W. M., and Bernstein, D. S., 1991, Robust stabilization with positive real uncertainty: beyond the small gain theorem. Systems Control Letters, 17, 191–208.
   Google Scholar
• Haddad, W. M., and Bernstein, D. S., 1994, Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle, and Popov theorems and their application to robust stability. Part II: discrete-time theory. International Journal of Robust and Nonlinear Control, 4, 249–265.
   Google Scholar
• Hinamoto, T., 1993, 2-D Lyapunov equation and filter design based on the Fornasini-Marchesini second model. IEEE Transactions on Circuits Systems I, 40, 102–110.
   Google Scholar
• Iwasaki, T., and Skelton, R. E., 1994, All controllers for the general H∞ control problems: LMI existence conditions and state space formulas. Automatica, 30, 1307–1317.
   Google Scholar
• Kaczorek, T., 1985, Two-Dimensional Linear Systems (Berlin: Springer-Verlag).
   Google Scholar
• Mahmoud, M. S.. Soh, Y. C, and Xie, L., 1999, Observer-based positive real control of uncertain linear systems. Automatica, 35, 749–754.
   Google Scholar
• Mahmoud, M. S., and Xie, L., 2000, Positive real analysis and synthesis of uncertain discrete time systems. IEEE Transactions on Circuits Systems, I, 47, 403–406.
   Google Scholar
• Owens, D. H., and Rogers, E., 1999, Stability analysis for a class of 2D continuous-discrete linear systems with dynamic boundary conditions. Systems and Control Letters, 37, 55–60.
   Google Scholar
• Roberts, P. D., 2000, Numerical investigations of a stability theorem arising from 2-dimensional analysis of an iterative optimal control algorithm. Multidimensional Systems and Signal Processing, 11, 109–124.
   Google Scholar
• Roesser, R. P., 1975, A discrete state-space model for linear image processing. IEEE Transactions on Automatic Control, 20, 1–10.
   Google Scholar
• Rogers, E., and Owens, D. H., 1992, Stability Analysis for Linear Repetitive Processes (Berlin: Springer-Verlag).
   Google Scholar
• Sun, W., Khargonekar, P. P., and Shim, D., 1994, Solution to the positive real control problem for linear time-invariant systems. IEEE Transactions on Automatic Control, 39, 2034–2046.
   Google Scholar
• Vidyasagar, M., 1993, Nonlinear Systems Analysis (Englewood Cliffs, NJ: Prentice-Hall).
   Google Scholar
• Wen, J. T., 1988, Time domain and frequency domain conditions for positive realness. IEEE Transactions on Automatic Control, 33, 988–992.
   Google Scholar
• Xie, L., and Soh, Y. C, 1995, Positive real control for uncertain linear time-invariant systems. Systems Control Letters, 24, 265–271.
   Google Scholar