Optimal control: linear quadratic methods
Optimal control: linear quadratic methods
Mixed H2/H∞ control for discrete-time systems via convex optimization
Automatica (Journal of IFAC) - Special issue on robust control
Analysis of Robust H2 Performance Using Multiplier Theory
SIAM Journal on Control and Optimization
Optimization by Vector Space Methods
Optimization by Vector Space Methods
A convex approach to robust H2 performance analysis
Automatica (Journal of IFAC)
| Hi-index | 22.15 |
Recently, a new deterministic characterization of the H"2 norm has been proposed, using a new norm (||.||"W"""@h), based on (approximate) set membership modeling of white noise. The main result shows that under mild conditions, for a fixed system the gap between the H"2 and W"@h norms can be made arbitrarily small. Motivated by these results it has been argued that the ||.||"W"""@h norm provides a useful tool for analyzing robust H"2 controllers, specially since in this context LMI-based necessary and sufficient conditions for robust performance are available. Unfortunately, as we show here with an example involving a very simple plant, the worst case ||.||"W"""@h"^"m norm can be conservative by at least a factor of m (where m denotes the dimension of the exogenous signal) for the original robust H"2 problem. Moreover, the same example shows that competing state-space based bounds also exhibit a similar degree of conservatism. Thus, at this point the problem of finding non-conservative bounds on the worst H"2 norm under LTI or slowly-varying LTV perturbations still remains open.