The united stable solution set of interval continuous-time algebraic Riccati equation and verified numerical computation of its outer estimation

Tayyebe HAQIRI; Mahmoud Mohseni MOGHADAM; Azim RIVAZ

Makale detayları

The united stable solution set of interval continuous-time algebraic Riccati equation and verified numerical computation of its outer estimation

Yazarlar:

Tayyebe HAQIRI | Mahmoud Mohseni MOGHADAM | Azim RIVAZ

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2018 Vol.42 Issue 3, pp.1130-1155

Belge Tipi:

Makale

Yayın Tarihi:

5/2018

Belge Dili:

Türkçe

Document ID (Org No.):

2000745873

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Özet:

 

This paper introduces the interval continuous-time algebraic Riccati equation A∗X+XA+Q−XGX=0A∗X+XA+Q−XGX=0\mathbf{A}^* X + X\mathbf{A} + \mathbf{Q} -X \mathbf{G} X=0, where A,GA,G\mathbf{A}, \mathbf{G}, and QQ\mathbf{Q} are known n×nn×nn \times n complex interval matrices, GG\mathbf{G} and QQ\mathbf{Q} are Hermitian, and XXX is an unknown matrix of the same size, and develops two approaches for enclosing the united stable solution set of this interval equation. We first discuss the united stable solution set and then derive a nonlinear programming method in order to find an enclosure for the united stable solution set. We also advance an efficient technique for enclosing the united stable solution set based on a variant of the Krawczyk method together with some modifications. These modifications enable us to reduce the computational complexity significantly. Various numerical experiments established upon a number of standard benchmark examples are also given to show the efficiency of this modified Krawczyk technique.

Makale detayları

The united stable solution set of interval continuous-time algebraic Riccati equation and verified numerical computation of its outer estimation

Yazarlar: Tayyebe HAQIRI | Mahmoud Mohseni MOGHADAM | Azim RIVAZ

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2018 Vol.42 Issue 3, pp.1130-1155

Belge Tipi: Makale

Yayın Tarihi: 5/2018

Belge Dili: Türkçe

Document ID (Org No.): 2000745873

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Tayyebe HAQIRI | Mahmoud Mohseni MOGHADAM | Azim RIVAZ

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2018 Vol.42 Issue 3, pp.1130-1155

Belge Tipi:

Makale

Yayın Tarihi:

5/2018

Belge Dili:

Türkçe

Document ID (Org No.):

2000745873

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098