Topic
Riccati equation
About: Riccati equation is a research topic. Over the lifetime, 10428 publications have been published within this topic receiving 210015 citations. The topic is also known as: Riccati's differential equation.
Papers published on a yearly basis
Papers
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TL;DR: In this paper, the linear integral equation for the solutions of the Korteweg-de Vries (KdV) equation is derived from the direct linearization of a general nonlinear difference-difference equation.
242 citations
TL;DR: In this paper, a pipe conveying fluid and a fluid loaded panel are studied from the viewpoint of differentiable dynamics, where non-linear terms are included and it is shown how the partial differential equation of motion can be recast, by Galerkin's method and modal truncation, in the form of an ordinary differential equation in Euclidean n -space.
240 citations
TL;DR: In this paper, a Riccati equation approach is proposed to solve the estimation problem and it is shown that the solution is related to two algebraic Riemannian equations, and the estimation error dynamics is quadratically stable and the induced operator norm is kept within a prescribed bound for all admissible uncertainties.
Abstract: SUMMARY This paper is concerned with the problem of Hm estimation for linear discrete-time systems with timevarying norm-bounded parameter uncertainty in both the state and output matrices. We design an estimator such that the estimation error dynamics is quadratically stable and the induced operator norm of the mapping from noise to estimation error is kept within a prescribed bound for all admissible uncertainties. A Riccati equation approach is proposed to solve the estimation problem and it is shown that the solution is related to two algebraic Riccati equations.
240 citations
TL;DR: In this article, the authors derived a 3-block form for the optimal filter and a corresponding 3block Riccati equation for a general class of time-varying descriptor models which need not represent a well-posed system in that the dynamics may be either over or under constrained.
Abstract: A general formulation of a discrete-time filtering problem for descriptor systems is considered. It is shown that the nature of descriptor systems leads directly to the need to examine singular estimation problems. Using a dual approach to estimation, the authors derive a so-called 3-block form for the optimal filter and a corresponding 3-block Riccati equation for a general class of time-varying descriptor models which need not represent a well-posed system in that the dynamics may be either over or under constrained. Specializing in the time-invariant case, they examine the asymptotic properties of the 3-block filter, and in particular analyze in detail the resulting 3-block algebraic Riccati equation. The noncausal nature of discrete-time descriptor dynamics implies that future dynamics may provide some information about the present state. A modified form for the descriptor Kalman filter that takes this information into account is presented. >
237 citations
TL;DR: The Riccati transformation of linear filtering/control theory is shown to be a contraction on the space of positive symmetric matrices as mentioned in this paper, which is used to describe the asymptotic behavior of the filter for systems with stochastic stationary parameters.
Abstract: The Riccati transformation of linear filtering/control theory is shown to be a contraction on the space of positive symmetric matrices. This is used to describe the asymptotic behavior of the filter for systems with stochastic stationary parameters.
236 citations