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 controllability of linear periodic systems and the existence of periodic solutions for periodic matrix Riccati equations are discussed, and a few problems playing a basic role in periodic control theory are discussed.
Abstract: Referring to recently published results, a few problems apparently playing a basic role in periodic control theory are discussed in this paper. Specifically, the problems dealt with are the controllability of linear periodic systems and the existence of periodic solutions for periodic matrix Riccati equations.
52 citations
TL;DR: The improved F-expansion method combined with Riccati equation is one of the most effective analytical methods in finding the exact traveling wave solutions to non-linear evolution equations in matrices as discussed by the authors.
Abstract: The improved F-expansion method combined with Riccati equation is one of the most effective analytical methods in finding the exact traveling wave solutions to non-linear evolution equations in mat...
52 citations
01 Mar 1995
TL;DR: In this article, a Riccati equation approach to the output feedback quadratic stabilisation of an uncertain system is presented, which involves the minimisation of a certain bound on an LQG cost function.
Abstract: The paper presents a Riccati equation approach to the output feedback quadratic stabilisation of an uncertain system. The uncertain systems under consideration depend on a norm-bounded time-varying matrix of uncertain parameters. A feature of the approach taken is that it involves the minimisation of a certain bound on an LQG cost function. The results were obtained by combining results on an optimal guaranteed cost linear quadratic regulator problem for uncertain systems and an optimal guaranteed cost state estimation problem for uncertain systems.
52 citations
TL;DR: By using the generalized Riccati transformation and the inequality technique, one new oscillation criterion is established for the second-order nonlinear delay dynamic equations on time scales.
Abstract: By using the generalized Riccati transformation and the inequality technique, we establish one new oscillation criterion for the second-order nonlinear delay dynamic equations on time scales. Our results not only extend and improve some known theorems, but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation on time scales.
52 citations
TL;DR: In this article, a new proof for the inequality tr (XY) \leq \parallel X ∈ {2} \cdot tr Y under the condition that X may be any square matrix.
Abstract: A new proof is presented for the inequality, tr (XY) \leq \parallel X \parallel_{2} \cdot tr Y . This argument is valid under the condition that Y be real symmetric nonnegative definite; X may be any square matrix.
52 citations