On Computing the Anisotropic Norm of Linear Discrete-Time-Invariant Systems

Anisotropy-based bounded real lemma for linear discrete-time descriptor systems

“…Excluding from consideration the trivial case where the function Λ in (20) is a constant matrix, A (q) and N (q) are both strictly increasing in q (see [14], [15]). This allows the minimum required mean anisotropy in (22) to be computed as A (N −1 (γ)), where N −1 denotes the functional inverse of N .…”

Stochastic robust controller reduction by anisotropic balanced truncation

“…is the mean anisotropy functional introduced in [1], and the angular boundary value G(ω) lim r→1−0 G(re iω ).…”

“…The lack of performance in terms of the anisotropic norm can be expressed as |||F e ||| α = |||F − F r ||| α , where F e is the error model, F is the closed-loop system defined by (4), F r = F l (P, K r ) is the closed-loop system with a reducedorder controller. This value can be computed following the way of [1].…”

“…The stochastic approach to H ∞ optimization introduced in [1], [2] is based on using the anisotropic norm of a system as performance criterion. This approach combines the attractive features of robust control and information theories holding an intermediate position between H 2 /LQG and H ∞ problems.…”

LMI-based design of multichannel anisotropic suboptimal controllers with application to control of gyrostabilized platform

“…is the mean anisotropy functional [3], [5]. Let T zw (z) denote the transfer function from W to Z of the closed-loop system with the fixed-order controller K(z) in the general dynamic compensator form…”