Robust and optimal control
Robust multi-objective feedback design by quantifier elimination
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Journal of Symbolic Computation - Special issue: applications of quantifier elimination
The Optimal H∞ Norm of a Parametric System Achievable Using a Static Feedback Controller
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Algebraic Approach to the Computation of the Defining Polynomial of the Algebraic Riccati Equation
CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
SyNRAC: a Maple-package for solving real algebraic constraints
ICCS'03 Proceedings of the 1st international conference on Computational science: PartI
Algebraic Approach to the Computation of the Defining Polynomial of the Algebraic Riccati Equation
CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
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The algebraic Riccati equation, which we denote by 'ARE' in the rest of the paper, is one of the most important equations of the post modern control theory. It plays important role for solving H 2 and H *** optimal control problems. Although a well-known numerical algorithm can compute the solution of ARE efficiently ([1],[2]) the algorithm can not be applied when a given system contains an unknown parameter. This paper presents an algorithm to compute the defining polynomial of an ARE with unknown parameter k . Such algorithm is also discussed in [3], where an algorithm with numerical approach is presented. The new algorithm in this paper uses algebraic approaches based on Groebner basis and resultant. Numerical experiments show the new algorithm is more efficient than that of [3] in most cases.