Quadratic guaranteed cost control for uncertain dissipative models: a Riccati equation approach

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.