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.
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TL;DR: In this article, the 2+1 dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada equation is decomposed into systems of integrable ordinary differential equations resorting to the nonlinearization of Lax pairs.
62 citations
TL;DR: If is an approximate solution of the equation, then there exists an exact solution of this equation near to .
Abstract: The aim of this paper is to prove the stability in the sense of Hyers-Ulam of differential equation of second order . That is, if is an approximate solution of the equation , then there exists an exact solution of the equation near to .
62 citations
01 Sep 1985
TL;DR: In this paper, a numerical procedure to determine the load-frequency control of a power system composed of several interconnected areas is proposed based on a new property of the classical Riccati equation which is analyzed in two different aspects: closed-loop asymptotic stability and suboptimality degree.
Abstract: In the paper we propose a numerical procedure to determine the load-frequency control of a power system composed of several interconnected areas. In order to decrease the associated implementation cost, the control law is constrained to have two different special structures: decentralised feedback and/or output feedback control. The procedure is based on a new property of the classical Riccati equation which is analysed in two different aspects: closed-loop asymptotic stability and suboptimality degree. An example of two interconnected areas is solved and comparisons are made in order to evaluate the performance of the closed-loop system.
62 citations
Journal Article•
TL;DR: An iterative algorithm to solve algebraic riccati equations with an indefinite quadratic term with superior effectiveness when compared with methods based on finding stable invariant subspaces of Hamiltonian matrices.
Abstract: An iterative algorithm to solve algebraic riccati equations with an indefinite quadratic term is proposed. The global convergence and local quadratic rate of convergence of the algorithm are guaranteed and a proof is given. Numerical examples are also provided to demonstrate the superior effectiveness of the proposed algorithm when compared with methods based on finding stable invariant subspaces of Hamiltonian matrices. A game theoretic interpretation of the algorithm is also provided.
62 citations
TL;DR: In this paper, an iterative reproducing kernel Hilbert space method is applied to get the solutions of fractional Riccati differential equations, and the analysis implemented in this work forms a crucial step in the process of developing fractional calculus.
Abstract: We apply an iterative reproducing kernel Hilbert space method to get the solutions of fractional Riccati differential equations. The analysis implemented in this work forms a crucial step in the process of development of fractional calculus. The fractional derivative is described in the Caputo sense. Outcomes are demonstrated graphically and in tabulated forms to see the power of the method. Numerical experiments are illustrated to prove the ability of the method. Numerical results are compared with some existing methods.
62 citations