Title :
New iterative algorithm for algebraic Riccati equation related to H ∞ control problem of singularly perturbed systems
Author :
Mukaidani, Hiroaki ; Xu, Hua ; Mizukami, Koichi
Author_Institution :
Fac. of Inf. Sci., Hiroshima Univ., Japan
fDate :
10/1/2001 12:00:00 AM
Abstract :
We present the solution to the algebraic Riccati equation (ARE) with indefinite sign quadratic term related to the H∞ control problem for singularly perturbed systems by means of a Kleinman type algorithm. The resulting algorithm is very efficient from the numerical point of view because the ARE is solvable even if the quadratic term has an indefinite sign. Moreover, the resulting iterative algorithm is quadratically convergent. We also present an algorithm for solving the generalized algebraic Lyapunov equation on the basis of the fixed point algorithm
Keywords :
H∞ control; Lyapunov matrix equations; Riccati equations; convergence of numerical methods; iterative methods; singularly perturbed systems; H∞ control problem; Kleinman type algorithm; algebraic Riccati equation; fixed point algorithm; generalized algebraic Lyapunov equation; iterative algorithm; quadratically convergent algorithm; singularly perturbed systems; Adaptive control; Automatic control; Constraint optimization; Control systems; Frequency; Genetic algorithms; Iterative algorithms; Polynomials; Riccati equations; Uncertainty;
Journal_Title :
Automatic Control, IEEE Transactions on
