Lower bounds on the solution of coupled algebraic Riccati equation

Abou-Kandil, 1994, Solution and asymptotic behavior of coupled Riccati equations in jump linear systems, IEEE Transactions on Automatic Control, 39, 1631, 10.1109/9.310038 Abou-Kandil, 1995, On the solution of discrete-time Markovian jump linear quadratic control problems, Automatica, 31, 765, 10.1016/0005-1098(94)00164-E Allwright, 1980, A Lower bound for the solution of the algebraic Riccati equation of optimal control and a geometric convergence for the Kleinman algorithm, IEEE Transactions on Automatic Control, 25, 826, 10.1109/TAC.1980.1102412 Boukas, 1997, Robust stabilization and guaranteed cost control of large scale linear systems with jumps, Kybernetika, 33, 121 Chizeck, 1986, Discrete-time Markovian-jump linear quadratic optimal control, International Journal of Control, 43, 213, 10.1080/00207178608933459 Czornik, 1997, On bound for the solution of the unified algebraic Riccati equation, Matematyka Stosowana, 40, 13 Czornik, 1997, On Upper bound for the unified algebraic Riccati equation, Systems and Control Letters, 32, 235, 10.1016/S0167-6911(97)00071-6 Czornik, A., & Swierniak, A. (2001). Upper bounds on the solution of coupled algebraic Riccati equation. Journal of Inequalities and Applications, accepted for publication. Gajic, Z., Qureshi, M. (1995). Lyapunov matrix equation in System stability and control. New York: Academic Press. Komaroff, 1989, Simultaneous eigenvalue lower bounds for the Riccati matrix equation, IEEE Transactions on Automatic Control, 34, 175, 10.1109/9.21091 Komaroff, 1996, On bounds for the solution of the Riccati equation for discrete-time control system, Control and Dynamics Systems, 76, 275, 10.1016/S0090-5267(96)80055-7 Kwon, 1996, Bounds in algebraic Riccati and Lyapunov equations: Survey and some new results, International Journal of Control, 64, 377, 10.1080/00207179608921634 Langholz, 1979, A new lower bound on the cost of optimal regulator, IEEE Transactions on Automatic Control, 24, 353, 10.1109/TAC.1979.1102020 Lee, 1995, A new approach for the robust stability of perturbed systems with class of non-commensurate time delays, IEEE Transactions on Circuits and systems, 40, 605 Marshall, 1979 Mori, 1994, A brief summary of the bounds on the solution of the algebraic matrix equations in control theory, International Journal of Control, 39, 247, 10.1080/00207178408933163 Mori, 1983, A way to stabilizable linear system with delayed state, Automatica, 19, 571, 10.1016/0005-1098(83)90013-4 Middleton, 1990 Mrabti, 1995, Bounds for the eigenvalues of the solution of the unified algebraic Riccati matrix equation, Systems and Control Letters, 24, 345, 10.1016/0167-6911(94)00048-Z Rami, 1996, LMI optimization for nonstandard Riccati equations arising in stochastic control, IEEE Transactions on Automatic Control, 41, 1666, 10.1109/9.544005 Patel, R. V., & Toda, M. (1980). Quantitative measures of robustness for multivariable systems. Proceedings of the Joint Automatic Control Conference, San Francisco, TP8-A. Wonham, W.M. (1971). Random differential equations in control theory. In A.T. Bharucha-Reid (Ed.), Probabilistic methods in applied mathematics (vol. 2). New York: Academic Press. Val, 1998, Uncoupled Riccati iterations for the linear quadratic control problem of discrete-time Markov jump linear systems, IEEE Transactions on Automatic Control, 43, 1727, 10.1109/9.736071