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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 paper, the necessary and sufficient condition for the existence of a unique, non-negative definite and periodic solution and the asymptotically stable closed-loop system is derived in terms of the stabilizability and detectability of matrix pairs, that is the natural generalization of those for constant matrix pairs.
Abstract: The matrix Riccati differential equation with periodic coefficients is discussed in this paper. As is well known, such equations are frequently encountered in the applications of the optimal filtering and control theory. The necessary and sufficient condition is derived for the existence of a unique, non-negative definite and periodic solution and the asymptotically stable closed-loop system. Such condition is stated in terms of the stabilizability and detectability of matrix pairs, that is the natural generalization of those for constant matrix pairs.

81 citations

Journal ArticleDOI
TL;DR: In this article, an improved generalized method for constructing multiple travelling wave solutions of nonlinear partial differential equations and implemented in a computer algebraic system was proposed. But the method was not applied to the KdV-type equations and the Kk-shaped solitons.
Abstract: Applying the improved generalized method, which is a direct and unified algebraic method for constructing multiple travelling wave solutions of nonlinear partial differential equations and implemented in a computer algebraic system, we consider the KdV-type equations and KdV–Burgers-type equations with nonlinear terms of any order. As a result, we can not only successfully recover the previously known travelling wave solutions found by existing various tanh methods and other sophisticated methods, but also obtain some new formal solutions. The solutions obtained include kink-shaped solitons, bell-shaped solitons, singular solitons and periodic solutions.

81 citations

Journal ArticleDOI
TL;DR: In this article, the authors make explicit connections between classical absolute stability theory and modern mixed-μ analysis and synthesis, using the parameter-dependent Lyapunov function framework of Haddad and Bernstein and the frequency dependent off-axis circle interpretation of How and Hall.
Abstract: In this paper we make explicit connections between classical absolute stability theory and modern mixed-μ analysis and synthesis. Specifically, using the parameter-dependent Lyapunov function framework of Haddad and Bernstein and the frequency dependent off-axis circle interpretation of How and Hall, we extend previous work on absolute stability theory for monotonic and odd monotonic nonlinearities to provide tight approximations for constant real parameter uncertainty. An immediate application of this framework is the generalization and reformulation of mixed-μ analysis and synthesis in terms of Lyapunov functions and Riccati equations. This observation is exploited to provide robust, reduced-order controller synthesis while avoiding the standard D, N - K iteration and curve-fitting procedures.

81 citations

Journal ArticleDOI
TL;DR: In this article, conditions for monotonic behavior of the solutions of the Riccati differential equation and the difference equation were derived without the usual requirement of detectability (respectively, stabilizability).
Abstract: Conditions, sufficient and necessary, for monotonic behavior of the solutions of the Riccati differential equation and Riccati difference equation are derived. For the optimal filtering (respectively, control) equation these results are derived without the usual requirement of detectability (respectively, stabilizability). The monotonic behavior allows proof of stabilizing properties of the solutions, subject only to requirements on the initial conditions. >

80 citations

Journal ArticleDOI
TL;DR: In this paper, conditions for the existence of a suitable state feedback are formulated in terms of a quadratic matrix inequality, reminiscent of the dissipation inequality of singular linear QoE optimal control.
Abstract: In this paper the standard $H_\infty $ control problem using state feedback is considered. Given a linear, time-invariant, finite-dimensional system, this problem consists of finding a static state feedback such that the resulting closed-loop transfer matrix has $H_\infty $ norm smaller than some a priori given upper bound. In addition it is required that the closed-loop system is internally stable. Conditions for the existence of a suitable state feedback are formulated in terms of a quadratic matrix inequality, reminiscent of the dissipation inequality of singular linear quadratic optimal control. Where the direct feedthrough matrix of the control input is injective, the results presented here specialize to known results in terms of solvability of a certain indefinite algebraic Riccati equation.

80 citations


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