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: This paper extends the algorithm in van Hoeij and Weil (1997) to compute semi-invariants and a theorem in Singer and Ulmer ( 1997) in such a way that, by computing one semi-Invariant that factors into linear forms, one gets all coefficients of the minimal polynomial of an algebraic solution of the Riccati equation, instead of only one coefficient.
70 citations
TL;DR: In this paper, the eigenvalues and sums and products of the Eigenvalues of the solution of the discrete Riccati and Lyapunov matrix equations and the continuous Lyapinov matrix equation were studied.
Abstract: We present some bounds for the eigenvalues and certain sums and products of the eigenvalues of the solution of the discrete Riccati and Lyapunov matrix equations and the continuous Lyapunov matrix equation. Nearly all of our bounds for the discrete Riccati equation are new. The bounds for the discrete and continuous Lyapunov equations give a completion of some known bounds for the extremal eigenvalues and the determinant and the trace of the solution of the respective equation.
70 citations
TL;DR: In this paper, it was shown that the existence of an internally stabilizing controller that makes the $H_ ∞ $ norm strictly less than 1 is related to stabilizing solutions to two algebraic Riccati equations.
Abstract: This paper is concerned with the discrete time $H_\infty $ control problem with measurement feedback. It follows that, as in the continuous time case, the existence of an internally stabilizing controller that makes the $H_\infty $ norm strictly less than 1 is related to the existence of stabilizing solutions to two algebraic Riccati equations. However, in the discrete time case, the solutions of these algebraic Riccati equations must satisfy extra conditions.
70 citations
TL;DR: In this article, two common collocation approaches based on radial basis functions (RBFs) have been considered; one is computed through the differentiation process (DRBF) and the other one is calculated through the integration process (IRBF).
70 citations
70 citations