STABLE – a stability algorithm for parametric model reduction by matrix interpolation

Figures & data

Figure 1. Convex cones ${\mathcal{C}}_1$ (left), ${\mathcal{C}}_2$ (right) and ${\mathcal{P}}_1,{\mathcal{P}}_2$.

Table 1. Comparison of the adjusted ROBs and of the respective minimum values of the objective functions for matrix interpolation with and without STABLE.

	Without STABLE	With STABLE
ROBs	${\tilde{\mathbf{V}}}_i^{\mathrm{W}\mathrm{S}}={\mathbf{V}}_0$	${\tilde{\mathbf{V}}}_i={\mathbf{V}}_0$
	${\tilde{\mathbf{W}}}_i^{\mathrm{W}\mathrm{S}}={\mathbf{W}}_0$	${\tilde{\mathbf{W}}}_i={\mathbf{W}}_0{\mathbf{P}}_i^{\ast }$
Objective functions	$J_{\mathbf{V},i}^{\mathrm{W}\mathrm{S}}({\mathbf{I}}_2)=0$	$J_{\mathbf{V},i}({\mathbf{I}}_2)=0$
	$J_{\mathbf{W},i}^{\mathrm{W}\mathrm{S}}({\mathbf{I}}_2)=0$	$J_{\mathbf{W},i}({\mathbf{P}}_i^{\ast })={0.303}^2$

Figure 2. Convex cones ${\mathcal{C}}_1$ (top left), ${\mathcal{C}}_2$ (bottom right) in the plane $p_{12,i}=0$ and optimal $(p_{11,i}^{\ast },p_{22,i}^{\ast })$ with minimum cost function $J_{\mathbf{W},i}={0.303}^2$.

Figure 3. Error $e_{{\mathcal{H}}_{\mathrm{\infty }}}^{{\mathcal{P}}_{\mathrm{t}\mathrm{e}\mathrm{s}\mathrm{t}}}$ without the stability-preserving method and the (a) MAC approach and the (b) DS approach.

Figure 4. Error $e_{{\mathcal{H}}_{\mathrm{\infty }}}^{{\mathcal{P}}_{test}}$ using STABLE and the (a) MAC approach and (b) DS approach.