Abstract. Many real processes can be modeled by stochastic differential equations with aftereffect [1]-[3]. Stability conditions for such systems can be obtained by construction of appropriate Lyapunov functionals using special procedure of Lyapunov functionals construction [4]-[14]. In this paper asymptotic mean square stability of stochastic linear differential equations with discrete and dis...

We present an algorithm for the solution of a nontrivial coupled system of algebraic Riccati equations appearing in risk sensitive control problems. Moreover we use comparison methods to derive non blow up conditions for the solutions of a corresponding terminal value problem for coupled systems of Riccati di erential equations.

The paper presents symplectic Möbius integrators for Riccati equations. All proposed methods preserve symmetry, positivity and quadratic invariants for the Riccati equations, and non-stationary Lyapunov functions. In addition, an efficient and numerically stable discretization procedure based on reinitialization for the associated linear Hamiltonian system is proposed.

based on symbolic manipulation program maple and using riccati equation mapping method several explicit exact solutions including kink, soliton-like, periodic and rational solutions are obtained for (2+1)-dimensional variable coefficient broer--kaup system in quite a straightforward manner. the known solutions of riccati equation are used to construct new solutions for variable coefficient broe...

State-dependent Riccati equation (SDRE) methods for designing control algorithms and observers for nonlinear processes entail the use of algebraic Riccati equations. These methods have yielded a number of impressive results, however, they can be computationally quite intensive and thus far they have not yielded to those attempting to assess their stability. This paper explores an alternative, t...

Modern optimal control techniques such as H2 and H1 control rely on the solution of algebraic Riccati equations for controller synthesis. Reliable numerical techniques for numerical computation of the solution of these equations have been proposed using eigenvector or Schur decompositions of Hamiltonian matrices for continuous-time algebraic Riccati equations (CARE), or symplectic matrices for ...