zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Stein iterations for the coupled discrete-time Riccati equations. (English) Zbl 1190.65066
Markovian jump linear systems (MJLS) are a class of models used to represent discrete jumps in continuous dynamics. This paper deals with iterative algorithms for computing solutions of a set of coupled algebraic Riccati equations that appears in quadratic optimal control problems for discrete-time MJLS. Two algorithms using decoupled Stein matrix equations are presented. A numerical example illustrates the proposed methods.

MSC:
65F30Other matrix algorithms
65F10Iterative methods for linear systems
93C55Discrete-time control systems
65K10Optimization techniques (numerical methods)
49N10Linear-quadratic optimal control problems
15A24Matrix equations and identities
WorldCat.org
Full Text: DOI
References:
[1] Costa, O. L. V; Aya, J. C. C.: Temporal difference methods for the maximal solution of discrete-time coupled algebraic ricacti equations. J. optim. Theory appl. 109, 289-309 (2001) · Zbl 0984.93051
[2] Costa, O. L. V; Marques, R. P.: Maximal and stabilizing Hermitian solutions for discrete-time coupled algebraic ricacti equations. Math. control signals systems 12, 167-195 (1999) · Zbl 0928.93047
[3] Costa, O. L. V; Fragoso, M. D.: Stability results for discrete-time linear systems with Markovian jumping parameters. J. math. Anal. appl. 179, 154-178 (1993) · Zbl 0790.93108
[4] Rami, M.; Ghaoui, L.: LMI optimization for nonstandard Riccati equations arising in stochastic control. IEEE trans. Automat. control. 41, No. 11, 1666-1671 (1996) · Zbl 0863.93087
[5] Gajic, Z.; Qureshi, M.: Lyapunov equation in system stability and control, series mathematics in science and engineering. (1995) · Zbl 1153.93300
[6] Borno, I.; Gajic, Z.: Parallel algorithm for solving coupled algebraic Lyapunov equations of discrete-time jump linear systems. Comput. math. Appl. 30, 1-4 (1995) · Zbl 0837.93075
[7] Ortega, J.; Rheinboldt, W.: Iterative solution of nonlinear equations in several variables. (1970) · Zbl 0241.65046
[8] Judd, K.: Numerical methods in economics. (1998) · Zbl 0924.65001
[9] Freiling, G.; Hochhaus, A.: Properties of the solutions of rational matrix difference equations. Comput. math. Appl. 45, 1137-1154 (2003) · Zbl 1055.39033
[10] Abou-Kandil, H.; Freiling, G.; Jank, G.: Solution and asymptotic behavior of coupled Riccati equations in jump linear systems. IEEE trans. Automat. control. 39, No. 8, 1631-1636 (1994) · Zbl 0925.93387
[11] Gajic, Z.; Borno, I.: Lyapunov iterations for optimal control of jump linear systems at steady state. IEEE trans. Automat. control 40, 1971-1975 (1995) · Zbl 0837.93073
[12] Barraud, A. Y.: A numerical algorithm to solve ATXA-X=Q. IEEE trans. Automat. control 22, 883-885 (1977) · Zbl 0361.65022