Perturbation Bounds and Characterisation of the Solution of the Associated Algebraic Riccati Equation
نویسندگان
چکیده
The paper deals with the associated algebraic matrix Riccati equation (AAMRE), closely related to the standard algebraic matrix Riccati equation arising in the theory of linear-quadratic optimisation and filtering. The sensitivity of the AAMRE relative to perturbations in its coefficients is studied. Both linear local (norm-wise and componentwise) and non-linear non-local perturbation bounds are obtained. The conditioning of the AAMRE is determined in particular. A full characterisation of the solution of AAMRE in terms of neutral subspaces of certain Hermitian matrix is given which is a counterpart of the characterisation of the solutions to the standard Riccati equation in terms of the invariant subspaces of the corresponding Hamiltonian matrix. A reliable method to obtain all solutions to AAMRE is briefly outlined.
منابع مشابه
A Solution of Riccati Nonlinear Differential Equation using Enhanced Homotopy Perturbation Method (EHPM)
Homotopy Perturbation Method is an effective method to find a solution of a nonlinear differential equation, subjected to a set of boundary condition. In this method a nonlinear and complex differential equation is transformed to series of linear and nonlinear and almost simpler differential equations. These set of equations are then solved secularly. Finally a linear combination of the solutio...
متن کاملOptimal integrated passive/active design of the suspension system using iteration on the Lyapunov equations
In this paper, an iterative technique is proposed to solve linear integrated active/passive design problems. The optimality of active and passive parts leads to the nonlinear algebraic Riccati equation due to the active parameters and some associated additional Lyapunov equations due to the passive parameters. Rather than the solution of the nonlinear algebraic Riccati equation, it is proposed ...
متن کاملBackward Perturbation Analysis of the Periodic Discrete-Time Algebraic Riccati Equation
Normwise backward errors and residual bounds for an approximate Hermitian positive semidefinite solution set to the periodic discrete-time algebraic Riccati equation are obtained. The results are illustrated by using simple numerical examples.
متن کاملAnalytical and Verified Numerical Results Concerning Interval Continuous-time Algebraic Riccati Equations
This paper focuses on studying the interval continuous-time algebraic Riccati equation A∗X + XA + Q − XGX = 0, both from the theoretical aspects and the computational ones. In theoretical parts, we show that Shary’s results for interval linear systems can only be partially generalized to this interval Riccati matrix equation. We then derive an efficient technique for enclosing the united stable...
متن کاملPerturbation Analysis of the Periodic Discrete-Time Algebraic Riccati Equation
This paper is devoted to the perturbation analysis for the periodic discrete-time algebraic Riccati equations (P-DAREs). Perturbation bounds and condition numbers of the Hermitian positive semidefinite solution set to the P-DAREs are obtained. The results are illustrated by numerical examples.
متن کامل