We consider a finite horizon linear discrete time varying system whose input is a random noise with an imprecisely known probability law. The statistical uncertainty is described by a nonnegative parameter a which constrains the anisotropy of the noise as an entropy theoretic measure of deviation of the actual noise distribution from Gaussian white noise laws with scalar covariance matrices. The worst-case disturbance attenuation capabilities of the system with respect to the statistically uncertain random inputs are quantified by the a-anisotropic norm which is a constrained operator norm of the system. We establish an anisotropic norm bounded real lemma which provides a state-space criterion for the a-anisotropic norm of the system not to exceed a given threshold. The criterion is organized as an inequality on the determinants of matrices associated with a difference Riccati equation and extends the Bounded Real Lemma of the H ∞ -control theory. We also provide a necessary background on the anisotropy-based robust performance analysis.

No abstract

Robust stochastic anisotropy-based H ∞ -optimization problem for discrete linear time-invariant (LTI) systems with structured parametric uncertainty is considered. It is shown that the problem can be reduced to mixed H 2 /H ∞ -like problem. The resulting control problem involves the minimization of anysotropic and H ∞ norms of the system. Explicit state-space formulas are also obtained for the optimal controller. The problem covers the standard H 2 /H ∞ optimization problem and H ∞ -optimization problem as two limiting cases.

No abstract

No abstract