Open AccessOn delay‐dependent algebraic Riccati equation
Author(s) -
Tan Cheng,
Wong Wing Shing,
Zhang Huanshui
Publication year - 2017
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2017.0233
Subject(s) - observability , algebraic riccati equation , riccati equation , mathematics , convergence (economics) , linear quadratic regulator , algebraic number , control theory (sociology) , algebraic solution , algebraic equation , controller (irrigation) , optimal control , control (management) , mathematical optimization , computer science , ordinary differential equation , mathematical analysis , nonlinear system , differential algebraic equation , differential equation , artificial intelligence , economic growth , quantum mechanics , physics , economics , biology , agronomy
This study presents a study on delay‐dependent algebraic Riccati equations (DAREs) derived from linear quadratic optimisation and stabilisation problems of networked control systems (NCSs) that endure both transmission delay and packet dropout. By applying the operator spectrum theory, two sets of fundamental results are obtained for such DARE: first, it is shown that the stabilising solution to a DARE, if it exists, is unique and coincides with a maximal solution. Moreover, under the assumption of detectability or observability, it is shown that the unique stabilising solution exists if and only if the associated NCS is stabilisable. Second, an iterative algorithm for computing the stabilising solution is proposed. The proof of convergence of the algorithm is presented. To confirm the validity of our theoretic results, two illustrative examples are included in this study. One of the example is motivated by a pursuit–evasion problem.