English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

The generalized version of the $mathcal{S}$-procedure, recently introduced by Iwasaki and co-authors and Scherer independently, has proved to be very useful for robustness analysis and synthesis of control systems. In particular, this procedure provides a nonconservative way to convert specific inequality conditions on lossless sets into numerically verifiable conditions represented by linear matrix inequalities (LMIs). In this paper, we introduce a new notion, one-vector-lossless sets, and propose a generalized $mathcal{S}$-procedure to reduce inequality conditions on one-vector-lossless sets into LMIs without any conservatism. By means of the proposed generalized $mathcal{S}$-procedure, we can examine various properties of matrix-valued functions over some regions on the complex plane. To illustrate the usefulness, we show that full rank property analysis problems of polynomial matrices over some specific regions on the complex plane can be reduced into LMI feasibility problems. It turns out that many existing results such as Lyapunov's inequalities and LMIs for state-feedback controller synthesis readily follow from the suggested generalized $mathcal{S}$-procedure

Generalized $\mathcal{S}$-Procedure for Inequality Conditions on One-Vector-Lossless Sets and Linear System Analysis