Discrete Riccati matrix equation and the order preserving property

Perturbation analysis of the discrete Riccati equation

The sensitivity of the discrete-time matrix Riccati equation relative to perturbations in its coefficients is studied. Both local and non-local perturbation bounds are obtained. In particular the conditioning of the equation is determined.

The discrete Riccati equation of optimal control

A review of the matrix Riccati equation

As usual, R denotes the field of real numbers, R" stands for the n-dimensional vector space over R, a prime denotes the transpose of a matrix, an asterisk denotes the complex conjugate transpose of a matrix, and P _ Q means that P — Q is hermitian or real symmetric nonnegative matrix. Square brackets represent matrices composed of the symbols inside. In order to get a better motivation for the ...

asymptotic property of order statistics and sample quntile

چکیده: فرض کنید که تابعی از اپسیلون یک مجموع نامتناهی از احتمالات موزون مربوط به مجموع های جزئی براساس یک دنباله از متغیرهای تصادفی مستقل و همتوزیع باشد، و همچنین فرض کنید توابعی مانند g و h وجود دارند که هرگاه امید ریاضی توان دوم x متناهی و امیدریاضی x صفر باشد، در این صورت می توان حد حاصلضرب این توابع را بصورت تابعی از امید ریاضی توان دوم x نوشت. حالت عکس نیز برقرار است. همچنین ما با استفاده...

Analytic properties of matrix Riccati equation solutions

For matrix Riccati equations of platoontype systems and of systems arising from PDEs, assuming the coefficients are analytic functions in a suitable domain, the analyticity of the stabilizing solution is proved under various hypotheses. In addition, general results on the analytic behavior of stabilizing solutions are developed. I. NONSTANDARD RICCATI EQUATIONS In [10], [7] and elsewhere contin...