Parallel algorithm for solving coupled algebraic Lyapunov equations of discrete-time jump linear systems

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...

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Veröffentlicht in:	Computers & mathematics with applications (1987) Jg. 30; H. 7; S. 1 - 4
Hauptverfasser:	Borno, I., Gajic, Z.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Oxford Elsevier Ltd 01.10.1995 Elsevier
Schlagworte:	Algorithms for functional approximation Coupled Lyapunov equations Discretetime systems Exact sciences and technology Jump linear systems Mathematical methods in physics Mathematics Methods of scientific computing (including symbolic computation, algebraic computation) Numerical analysis Numerical analysis. Scientific computation Numerical approximation and analysis Numerical linear algebra Parallel algorithms Physics Sciences and techniques of general use Jump linear systems Parallel algorithms Discretetime systems Coupled Lyapunov equations Algebraic equation Parallel algorithm Linear system Lyapunov equation Discrete time Equation system
ISSN:	0898-1221, 1873-7668
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Abstract	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 of unique positive solutions.
AbstractList	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 of unique positive solutions.
Author	Borno, I. Gajic, Z.
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References	Wachspress (BIB3) 1988; 1 Kumar, Varaiya (BIB5) 1986 Kantorovich, Akilov (BIB6) 1964 Bartels, Stewart (BIB2) 1972; 15 Chizeck, Willsky, Castanon (BIB1) 1986; 43 Lu, Wachspress (BIB4) 1991; 21 Kumar (10.1016/0898-1221(95)00119-J_BIB5) 1986 Bartels (10.1016/0898-1221(95)00119-J_BIB2) 1972; 15 Wachspress (10.1016/0898-1221(95)00119-J_BIB3) 1988; 1 Kantorovich (10.1016/0898-1221(95)00119-J_BIB6) 1964 Lu (10.1016/0898-1221(95)00119-J_BIB4) 1991; 21 Chizeck (10.1016/0898-1221(95)00119-J_BIB1) 1986; 43
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SubjectTerms	Algorithms for functional approximation Coupled Lyapunov equations Discretetime systems Exact sciences and technology Jump linear systems Mathematical methods in physics Mathematics Methods of scientific computing (including symbolic computation, algebraic computation) Numerical analysis Numerical analysis. Scientific computation Numerical approximation and analysis Numerical linear algebra Parallel algorithms Physics Sciences and techniques of general use
Title	Parallel algorithm for solving coupled algebraic Lyapunov equations of discrete-time jump linear systems
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