Abstract
We consider a set of continuous algebraic Riccati equations with indefinite quadratic parts that arise in H￥ control problems. It is well known that the approach for solving such type of equations is proposed in the literature. Two matrix sequences are constructed. Three effective methods are described for computing the matrices of the second sequence, where each matrix is the stabilizing solution of the set of Riccati equations with definite quadratic parts. The acceleration modifications of the described methods are presented and applied. Computer realizations of the presented methods are numerically compared. In addition, a second iterative method is proposed. It constructs one matrix sequence which converges to the stabilizing solution to the given set of Riccati equations with indefinite quadratic parts. The convergence properties of the second method are commented. The iterative methods are numerically compared and investigated.
Highlights
The algebraic Riccati equations with indefinite quadratic part have been investigated intensively
We show that the second iterative method constructs a convergent matrix sequence
In our investigation we present a few iterative methods for finding the stabilizing solution to (5)
Summary
The algebraic Riccati equations with indefinite quadratic part have been investigated intensively. The paper of Lanzon et al [1] is the first where is investigated an algebraic Riccati equation with an indefinite quadratic part in the deterministic case. How to find the stabilizing solution of the coupled algebraic Riccati equations of the optimal control problem for jump linear systems with indefinite quadratic part:. The main idea is to construct two matrix sequences such that the sum of corresponding matrices converges to the stabilizing solution of the set of Riccati Equation (1). Such approach is considered in [2]. We show that the second iterative method constructs a convergent matrix sequence. If the sufficient conditions of the first approach are satisfied the second iterative method converges
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