D. Arzelier et D. Peaucelle, Quadratic guaranteed cost control for uncertain dissipative models: a Riccati equation approach, INT J CONTR, 73(9), 2000, pp. 762-775
The problem of H-2 guaranteed cost control and dynamic output-feedback for
linear uncertain systems with dissipative uncertainty is addressed. The pro
blem of robust H-2 synthesis has been open for the last two decades. In thi
s payer, a problem of Hz quadratic guaranteed cost control is defined for u
ncertain systems affected by LTI quadratic dissipative model uncertainty. A
necessary and sufficient condition of quadratic stabilizability via output
-feedback is derived in terms of two coupled parameter-dependent Riccati eq
uations. Then, a method is given to design controllers which minimize an up
per bound for the worst-case H-2 norm of the uncertain system. It therefore
assesses a guaranteed level of robust performance where in literature, onl
y nominal performance is ensured in most cases. A reliable numerical iterat
ive procedure based on Riccati solvers and one-dimensional convex parameter
search is provided. With this uncertainty modelling and the developped num
erical procedure, we hope to reduce the usual conservatism of quadratic des
igns.