Related papers: The Riccati Characteristic Equation
Several instances of integrable Riccati equations are analyzed from the geometric perspective of the theory of Lie systems. This provides us a unifying viewpoint for previous approaches.
Solving large-scale continuous-time algebraic Riccati equations is a significant challenge in various control theory applications. This work demonstrates that when the matrix coefficients of the equation are quasiseparable, the solution…
Three comparison criteria are obtained for second order Riccati equations. On the basis of these criteria some global existence theorems are proved mentioned equations. The results obtained are used to derive a non oscillation criterion for…
The solvability of equilibrium Riccati equations (EREs) plays a central role in the study of time-inconsistent stochastic linear-quadratic optimal control problems, because it paves the way to constructing a closed-loop equilibrium…
Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyse a geometric method to construct integrability conditions for Riccati equations following these approaches. This approach provides…
New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…
The scalar Riccati equation is a prototypical nonlinear ODE having diverse mathematical connections. In the centuries since its initial formulation, a standard textbook theory has emerged according to which the general solution may be…
A consistent Riccati expansion (CRE) is proposed for solving nonlinear systems with the help of a Riccati equation. A system is defined to be CRE solvable if it has a CRE. Various integrable systems are CRE solvable. Furthermore, it is also…
The nonstandard Lagrangian representations of Ricatti and Riccati-type equations that exist in the literature cannot be obtained using Helmholtz solution of the inverse problem. In this work we consider Riccati and higher-order Riccati…
This paper proposes a novel iterative algorithm to compute the stabilizing solution of regime-switching stochastic game-theoretic Riccati differential equations with periodic coefficients. The method decomposes the original complex…
The Riccati equation method is used to establish some new stability criteria for systems of two linear first-order ordinary differential equations. It is shown that two of these criteria in the two dimensional case imply the Routh -…
The Riccati equations reducible to first-order linear equations by an appropriate change the dependent variable are singled out. All these equations are integrable by quadrature. A wide class of linear ordinary differential equations…
This work presents a newly renovated approach to the analysis of second-order Riccati equations from the point of view of the theory of Lie systems. We show that these equations can be mapped into Lie systems through certain Legendre…
Matrix Riccati equations and other nonlinear ordinary differential equations with superposition formulas are, in the case of constant coefficients, shown to have the same exact solutions as their group theoretical discretizations. Explicit…
The purpose of this paper is to investigate the role that the continuous-time generalised Riccati equation plays within the context of singular linear-quadratic optimal control. This equation has been defined following the analogy with the…
The Riccati equation method is used to establish a new stability criteria for linear systems of ordinary differential equations. Two examples are presented in which the obtained result is compared with the results obtained by the Lyapunov…
In this study, a recursive solution technique in conjunction with generalized integrating factors is presented and applied to address first and second order linear differential equations. This approach demonstrates practical utility in…
New integrability properties of a family of sequences of ordinary differential equations, which contains the Riccati and Abel chains as the most simple sequences, are studied. The determination of n generalized symmetries of the nth-order…
We study a differential Riccati equation (DRE) with indefinite matrix coefficients, which arises in a wide class of practical problems. We show that the DRE solves an associated control problem, which is key to provide existence and…
The Riccati equation method is used for study the oscillatory and non oscillatory behavior of solutions of systems of two first order linear two by two dimensional matrix differential equations. An integral and an interval oscillatory…