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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
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Journal ArticleDOI
TL;DR: In this article, the total hierarchy of the Kadomtsev-Petviashvili (KP) equation is transformed to a system of linear partial differential equations with constant coefficients, and complete integrability of the KP equation is proved by using this linear system.

102 citations

Journal ArticleDOI
TL;DR: In this brief, infinite-horizon nonlinear regulation of second-order systems using the State Dependent Riccati Equation (SDRE) method is considered and a relatively straightforward condition for global asymptotic stability of the closed-loop system is derived.
Abstract: In this brief, infinite-horizon nonlinear regulation of second-order systems using the State Dependent Riccati Equation (SDRE) method is considered. By a convenient parametrization of the A(x) matrix, the state-dependent algebraic Riccati equation is solved analytically. As a result, the closed-loop system equations are obtained in analytical form. Global stability analysis is performed by a combination of Lyapunov analysis and LaSalle's Principle. Accordingly, a relatively straightforward condition for global asymptotic stability of the closed-loop system is derived. This is one of the first global results available for this class of systems controlled by SDRE methods. The stability results are demonstrated on an experimental magnetic levitation setup and are found to provide a great deal of flexibility in the control system design.

102 citations

Journal ArticleDOI
TL;DR: In this article, the authors used the state-dependent Riccati equation (SDRE) to solve the problem of suboptimal dive plane control of autonomous underwater vehicles (AUVs).

101 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that the set of real symmetric solutions of the Riccati equation is isomorphic to the algebraic variety of invariant subspaces of a related matrix.
Abstract: We prove that the set of real symmetric solutions of the algebraic Riccati equation is isomorphic to the algebraic variety of invariant subspaces of a related $n \times n$ matrix. By characterizing the structure of this variety, we obtain a detailed description of the geometric properties of the solution set of the algebraic Riccati equation.

101 citations

Journal ArticleDOI
TL;DR: The structure-preserving doubling algorithm is developed from a new point of view and its quadratic convergence under assumptions which are weaker than stabilizability and detectability are shown, as well as practical issues involved in the application of the SDA to CAREs.

101 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023153
2022335
2021203
2020240
2019223
2018231