Riccati equations and Lie series

Liénard and Riccati Differential Equations Related via Lie Algebras

In this work we study the Liénard systems that can be transformed into Riccati differential equations, using changes of variables more general than the ones used by the classical Lie theory.

Reproducing Kernels and Riccati Equations

The purpose of this article is to present a brief exposition of the role of Riccati equations in the theory of reproducing kernel spaces. In particular, we shall exhibit a connection between positive semidefinite solutions of matrix Riccati equations and a class of finite dimensional reproducing kernel Hilbert spaces of rational vector valued functions, and an analogous (but more general) conne...

Lie and Riccati Linearization of a Class of Liénard Type Equations

1 Department of Mathematics, Eastern University, Chenkalady 30350, Sri Lanka 2 International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa 3 Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathemat...

Algebraic Riccati equations

Riccati Equations in Delay Systems

We give an overview of how the Riccati equation makes its appearance in the stability analysis of linear systems with delays. We avoid complexities as time-invariance, added perturbations, distributed delays etc, to get to the main issues. Most generalizations can be or have been carried out, but do not add substantially to our understanding. We also show the connection between quadratic stabil...