© The Institution of Engineering and Technology
The authors investigate the numerical solution of a set of discretetime generalised Riccati equations. The class of discretetime nonlinear equations involves in various control problems for discretetime stochastic systems and it can be considered as an important tool for solving optimisation control for such type systems. A new procedure for computing the maximal solution and the stabilising solution is proposed by Dragan et al. (‘Iterative algorithm to compute the maximal and stabilising solutions of a general class of discretetime Riccatitype equations’, Int. J. Control, 2010, 83, (4), pp. 837–847). In this study, the authors introduce a new iterative procedure based on the solution of a Stein matrix equation for computing the maximal and the stabilising solution. The convergence properties of the new iteration are proved. Sufficient conditions for computing the maximal solution and the stabilising solution are derived. Finally, some numerical examples are presented to illustrate the feasibility of the proposed algorithm.
References


1)

O.L.V. Costa
.
Meansquare stabilizing solutions for discrete time coupled algebraic Riccati equations.
IEEE Trans. Autom. Control
,
593 
598

2)

O.L. Costa ,
M.D. Fragoso ,
R.P. Marques
.
(2005)
Discretetime Markov jump linear systems.

3)

V. Dragan ,
T. Morozan
.
Discretetime Riccati type equations and the tracking problem.
ICIC Express Lett.
,
2 ,
109 
116

4)

G. Freiling ,
A. Hochhaus
.
Properties of the solutions of rational matrix difference equations.
Comput. Math. Appl.
,
1137 
1154

5)

Y. Ji ,
H.J. Chizeck ,
X. Feng ,
K.A. Loparo
.
Stability and control of discretetime jump linear systems.
Control Theory Adv. Technol.
,
247 
270

6)

T. Morozan
.
Stabilization of some stochastic discretetime control systems.
Stoch. Anal. Appl.
,
89 
116

7)

T. Morozan
.
Stability and control for linear systems with jump Markov perturbations.
Stoch. Anal. Appl.
,
91 
110

8)

V. Dragan ,
T. Morozan
.
A Class of discrete time generalized Riccati equations.
J. Differ. Equ. Appl.
,
4 ,
291 
320

9)

V. Dragan ,
T. Morozan ,
A. Stoica
.
Iterative algorithm to compute the maximal and stabilising solutions of a general class of discretetime Riccatitype equations.
Int. J. Control
,
4 ,
837 
847

10)

V. Dragan ,
T. Morozan
.
The linear quadratic optimization problem for a class of discretetime stochastic linear systems.
Int. J. Innov. Comput. Inf. Control
,
4 ,
2127 
2137

11)

V. Dragan ,
T. Morozan ,
A. Stoica
.
(2010)
Mathematical methods in robust control of discretetime linear stochastic systems.

12)

I.G. Ivanov
.
Stein iterations for the coupled discretetime Riccati equations.
Nonlinear Anal. Theory, Methods Appl.
,
6244 
6253

13)

V. Dragan ,
I. Ivanov
.
A numerical procedure to compute the stabilising solution of game theoretic Riccati equations of stochastic control.
Int. J. Control
,
4 ,
783 
800

14)

P. Lancaster ,
M. Tismenetsky
.
(1985)
The theory of matrices with applications.

15)

P. Lancaster ,
L. Rodman
.
(1995)
Algebraic Riccati equations.
http://iet.metastore.ingenta.com/content/journals/10.1049/ietcta.2011.0463
Related content
content/journals/10.1049/ietcta.2011.0463
pub_keyword,iet_inspecKeyword,pub_concept
6
6