In this paper, we consider the hermitian Riccati difference equations. Analogous to a differential equation, there is connection between equation and its associated linear equation. Based on can obtain an explicit representation for solution of define extended solution. Further, characterize asymptotic state rate convergence. Constant equilibrium solutions, periodic solutions closed limit cycle...

By considering the three-dimensional incompressible Euler equations, a 4-vector ζ is constructed out of a combination of scalar and vector products of the vorticity ω and the vortex stretching vector ω · ∇u = Sω. The evolution equation for ζ can then be cast naturally into a quaternionic Riccati equation. This is easily transformed into a quaternionic zero-eigenvalue Schrödinger equation whose ...

We discuss a parallel algorithm for the solution of large-scale generalized algebraic Riccati equations with dimension up to O(10). We survey the numerical algorithms underlying the implementation of the method, in particular, a Newton-type iterative solver for the generalized Riccati equation and an LR-ADI solver for the generalized Lyapunov equation. Experimental results on a cluster of Intel...

This paper investigates the problems of robust exponential stability and stabilization for uncertain linear non-autonomous control systems with discrete and distributed time-varying delays. Based on combination of the Riccati differential equation approach, linear matrix inequality (LMI) techinque and the use of suitable Lyapunov-Krasovskii functional, new sufficient conditions for the robust e...

Abstract. We study an algorithm for the numerical solution of algebraic matrix Riccati equations that arise in linear optimal control problems. The algorithm can be considered to be a multishift technique, which uses only orthogonal symplectic similarity transformations to compute a Lagrangian invariant subspace of the associated Hamiltonian matrix. We describe the details of this method and co...

In this paper, the time-consistent solutions of a timeinconsistent discrete-time stochastic linear-quadratic optimal control are investigated. Different from the existing literature, the definiteness constraint is not posed on the state and the control weight matrices of the cost functional. Necessary and sufficient conditions are, respectively, obtained to the existence of the open-loop time-c...