On solvability and numerical solutions of parameter-dependent differential matrix inequality
Atsumi Ohara, Y. Sasaki · Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228) · 2003
This paper considers the solvability condition and numerical algorithm for parameter-dependent differential affine matrix inequality. When the coefficient and solution matrices are assumed to be in a trigonometric polynomial form of the fixed order, the necessary and sufficient solvability condition is given in terms of linear matrix inequalities. The result is based on a simple idea making use of the positive real lemma to preserve positivity on an interval. Multidimensional parameter cases are also discussed.