We consider the question of robust stability of a linear
time invariant plant subject to dynamic perturbations, which are
dissipative in the sense of Willems with respect to several
quadratic supply rates. For instance, parasitic dynamics are often
both frequency weighted small gain and passive, and including
this in the robustness analysis results in conditions that are less
conservative than for instance the small gain criterion.
We reduce several robustness analysis questions to Linear Matrix
Inequalities: Robust stability, robust stability in presence of
parameter uncertainty, robust H-2 performance, and finally robust
performance in presence of disturbances with finite signal-to-noise
ratio in the sense of Skelton.
The corresponding problem of static state feedback controller design
reduces to non-convex matrix inequalities, which only in special
cases can be transformed to convex ones. We suggest heuristic
coordinate descent type algorithms to solve these problems.
IMM Technical Report 1/97
Last modified April 8, 1997
For further information, please contact, Finn Kuno
Christensen, IMM, Bldg. 321, DTU Phone: (+45) 4588 1433. Fax: (+45) 4588
2673, E-mail: fkc@imm.dtu.dk
