On computing the stabilizing solution of a class of discrete‐time periodic Riccati equations

Drăgan, Vasile; Aberkane, Samir; Ivanov, Ivan Ganchev

doi:10.1002/rnc.3131

Cited by 7 publications

(11 citation statements)

References 13 publications

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“…Our investigation is based on the theory of periodic discrete-time Riccati equations as well as on the iterative methods described in [7]. Dragan et al [7,8] study two iterative processes for the computation of the stabilizing solution to Equation (1) and derive their convergence properties. However, the proposed iterative methods are not investigated numerically.…”

Section: X(t) = R(t X) := a T (T)x(t + 1)a(t) − A T (T)x(t + 1)b(t) mentioning

confidence: 99%

“…In this paper we consider two iterative methods (Block Successive Approximations and A Block Stein Iteration) so as to develop numerical procedures (derived in [7,8]) for computing the stabilizing solution of a set of periodic discrete-time Riccati equations.…”

Section: X(t) = R(t X) := a T (T)x(t + 1)a(t) − A T (T)x(t + 1)b(t) mentioning

confidence: 99%

“…of Equation (1), which is described in Section 3.1 of the paper of Dragan and co-authors [7]. In fact, the iterative procedure is based on the solution to θ -periodic discrete-time Riccati equation with definite quadratic part:…”

Section: The Iterative Procedures With Two Matrix Sequencesmentioning

confidence: 99%

“…of Equation (1) is derived in [8]. The method preserves similar desirable characteristics as global convergence and local quadratic rate of convergence.…”

Section: The Iterative Procedures With One Matrix Sequencesmentioning

confidence: 99%

“…There are different methods to solve the periodic Riccati equations with a definite quadratic part [5,6]. Recently, [7,8] two iterative procedures have been developed for numerical computation of the stabilizing solution of a class of periodic discrete-time Riccati equation with an indefinite sign of it's quadratic term.…”

Section: Introductionmentioning

confidence: 99%

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The Iterative Solution to Discrete-Time H∞ Control Problems for Periodic Systems

Ivanov¹,

Bogdanova²

2016

Algorithms

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This paper addresses the problem of solving discrete-time H ∞ control problems for periodic systems. The approach for solving such a type of equations is well known in the literature. However, the focus of our research is set on the numerical computation of the stabilizing solution. In particular, two effective methods for practical realization of the known iterative processes are described. Furthermore, a new iterative approach is investigated and applied. On the basis of numerical experiments, we compare the presented methods. A major conclusion is that the new iterative approach is faster than rest of the methods and it uses less RAM memory than other methods.

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Section: X(t) = R(t X) := a T (T)x(t + 1)a(t) − A T (T)x(t + 1)b(t) mentioning

confidence: 99%

Section: X(t) = R(t X) := a T (T)x(t + 1)a(t) − A T (T)x(t + 1)b(t) mentioning

confidence: 99%

Section: The Iterative Procedures With Two Matrix Sequencesmentioning

confidence: 99%

“…of Equation (1) is derived in [8]. The method preserves similar desirable characteristics as global convergence and local quadratic rate of convergence.…”

Section: The Iterative Procedures With One Matrix Sequencesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Iterative Solution to Discrete-Time H∞ Control Problems for Periodic Systems

Ivanov¹,

Bogdanova²

2016

Algorithms

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A new methodology to compute stabilizing control laws for continuous‐time LTV systems

Agulhari

García

Tarbouriech

et al. 2018

Intl J Robust & Nonlinear

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Summary This paper is devoted to the problem of computing control laws for the stabilization of continuous‐time linear time‐varying systems. First, a necessary and sufficient condition to assess the stability of a linear time‐varying system based on the norm of the transition matrix computed over a sequence of successive finite‐time intervals is proposed. A link with a stability condition for an equivalent discrete‐time model is also established. Then, 3 approaches for the computation of stabilizing state‐feedback gains are proposed: a continuous‐time technique, ie, directly derived from the stability condition, not suitable for numerical implementation; a method based on the stabilization of the discrete‐time equivalent model along with a transformation to generate the desired continuous‐time gain; and the computation of stabilizing gains for a set of periodic discrete‐time systems. Finally, by adapting one of the existing methods for the stabilization of periodic discrete‐time systems, an algorithm for the computation of a stabilizing state‐feedback continuous‐time gain is proposed. A numerical example illustrates the validity of the technique.

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The iterative solution to LQ zero-sum stochastic differential games

Ivanov

2017

J. Appl. Math. Comput.

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On computing the stabilizing solution of a class of discrete‐time periodic Riccati equations

Cited by 7 publications

References 13 publications

The Iterative Solution to Discrete-Time H∞ Control Problems for Periodic Systems

The Iterative Solution to Discrete-Time H∞ Control Problems for Periodic Systems

A new methodology to compute stabilizing control laws for continuous‐time LTV systems

The iterative solution to LQ zero-sum stochastic differential games

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