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:
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