Lyapunov approach to robust pole-assignment analysis

Robust matrix 𝒟U‐stability analysis

“…Those results were later improved in References [22][23][24]. They were also extended to classes of regions that are usually connected (often even convex) and symmetric with respect to the real axis (let us just say 'symmetric') [25][26][27][28][29][30]. These bounds are deduced from necessary and sufficient conditions for nominal matrix root-clustering based, for example, on generalized Lyapunov equations [31], on the notion of logarithmic norms [32] or on LMI frame-work [13,12].…”

Robust -stability of discrete and continuous time interval systems

“…Moreover, the regional stability robustness with respect to Fig. 4 has been addressed in [14][15][16]. The robust D-stability of interval systems is considered in this paper.…”

“…Therefore, the robust Dstability problem is essentially a performance robustness problem in which the robust stability problem becomes a special case. During the past years, the problem of D-stability robustness has been an active area of research and different approaches have been proposed [10][11][12][13][14][15][16]. The analysis of D-stability robustness in a specified disk has been discussed in [10][11][12][13].…”

A Robust Design Method of Active Controller for Uncertain Vibration Systems

“…As is known, the dynamic characteristics of a system are related to the locations of their eigenvalues; one of the most important methods for the RAVC design is to assign all the eigenvalues of uncertain systems in a specified region so as to achieve the desired characteristics. Some techniques for eigenvalue assignment, such as Lyapunov approach, linear matrix inequality (LMI) design, Hankel matrix measure, and so on, have been presented (Juang, Hong, and Wang, 1989;Wang and Lin, 1992;Wang and Mau, 1995;Wiesel, 1995;Chilali and Gahinet, 1996). One drawback of these control strategies is that they are numerically very difficult to be realized, and sometimes the control loop should be redesigned thoroughly to meet the robustness requirement.…”