In mathematics, a Riccati equation is any ordinary differential equation that is quadratic in the unknown function. In other words, it is an equation of the form
where and . If the equation reduces to a Bernoulli equation, while if the equation becomes a first order linear ordinary differential equation.
The equation is named after Count Jacopo Francesco Riccati (1676–1754).
More generally, the term "Riccati equation" is used to refer to matrix equations with an analogous quadratic term, which occur in both continuous-time and discrete-time linear-quadratic-Gaussian control. The steady-state (non-dynamic) version of these is referred to as the algebraic Riccati equation.
Read more about Riccati Equation: Reduction To A Second Order Linear Equation, Application To The Schwarzian Equation, Obtaining Solutions By Quadrature
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