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The united stable solution set of interval continuous-time algebraic Riccati equation and verified numerical computation of its outer estimation. (English) Zbl 1424.65051

Summary: This paper introduces the interval continuous-time algebraic Riccati equation \(\mathbf{A}^* X + X\mathbf{A} + \mathbf{Q} -X \mathbf{G} X=0\), where \(\mathbf{A}, \mathbf{G}\), and \(\mathbf{Q}\) are known \(n \times n\) complex interval matrices, \(\mathbf{G}\) and \(\mathbf{Q}\) are Hermitian, and \(X\) 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.

MSC:

65F30 Other matrix algorithms (MSC2010)
15A24 Matrix equations and identities
65G30 Interval and finite arithmetic

Software:

INTLAB; mftoolbox
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Full Text: DOI

References:

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