Parallel algorithm for solving coupled algebraic Lyapunov equations of discrete-time jump linear systems. (English) Zbl 0837.93075
Summary: A parallel iterative scheme for solving coupled algebraic Lyapunov equations of discrete-time jump linear systems with Markovian transitions is introduced. The algorithm is computationally efficient since it operates on reduced-order decoupled algebraic discrete Lyapunov equations. Furthermore, the solutions at every iteration are computed by elementary matrix operations. Hence, the number of operations is minimal. Monotonicity of convergence is established under the existence conditions about unique positive solutions.
MSC:
| 93E25 | Computational methods in stochastic control (MSC2010) |
| 91A60 | Probabilistic games; gambling |
| 93E15 | Stochastic stability in control theory |
| 93C55 | Discrete-time control/observation systems |
Keywords:
coupled algebraic Lyapunov equations; discrete-time jump linear systems; Markovian transitionsSoftware:
Algorithm 432References:
| [1] | Chizeck, H. J.; Willsky, A. S.; Castanon, D., Discrete-time Markovian jump linear quadratic optimal control, Int. J. Contr., 43, 1, 213-231 (1986) · Zbl 0591.93067 |
| [2] | Bartels, R. H.; Stewart, G. W., Solution of the matrix equation \(AX + XB = C\), Communications of the ACM, 15, 820-826 (1972) · Zbl 1372.65121 |
| [3] | Wachspress, E., Iterative solution of the Lyapunov matrix equation, Appl. Math. Lett., 1, 1, 87-90 (1988) · Zbl 0631.65037 |
| [4] | Lu, A.; Wachspress, E., Solution of Lyapunov equations by alternating direction implicit iterations, Computers Math. Applic., 21, 9, 43-58 (1991) · Zbl 0724.65041 |
| [5] | Kumar, P. R.; Varaiya, P., Stochastic Systems: Estimation, Identification, and Adaptive Control (1986), Prentice Hall: Prentice Hall Englewood Cliffs, NJ · Zbl 0706.93057 |
| [6] | Kantorovich, L.; Akilov, G., Functional Analysis in Normed Spaces (1964), Macmillan: Macmillan New York · Zbl 0127.06104 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
