A μ-analysis based approach to probabilistic delay margin analysis of uncertain linear systems*

Attitude control laws validation through probabilistic µ-analysis : application to a microsatellite control laws

“…During the past 5 years, a significant effort has been put in the development of probabilistic μ theory and its implementation in the Matlab STOchastic Worst-case Analysis Toolbox (STOWAT) [9]. Stability and 𝐻 ∞ performance were studied first [7,8], followed by gain/phase/disk margins [10] and more recently delay margin [11]. The theory behind μ-analysis is not presented in this paper due to space limitations, but the interested reader can for example refer to [1,2,12] and [3][4][5][6][7][8][9][10][11] for the classical and the probabilistic versions respectively.…”

“…Stability and 𝐻 ∞ performance were studied first [7,8], followed by gain/phase/disk margins [10] and more recently delay margin [11]. The theory behind μ-analysis is not presented in this paper due to space limitations, but the interested reader can for example refer to [1,2,12] and [3][4][5][6][7][8][9][10][11] for the classical and the probabilistic versions respectively. Only a few facts are briefly recalled below to facilitate the understanding of the paper.…”

“…smaller) than the desired threshold 𝜙, it is then checked whether the margin requirement is satisfied (resp. violated) on the entire domain ℬ 𝛿 , using sufficient conditions involving μ upper bound computations (see Propositions 3.1 and 3.3 of [10] for gain/phase/disk margins, and Propositions 4.1 and 4.3 of [11] for delay margin). If this cannot be guaranteed, ℬ 𝛿 is finally partitioned into smaller boxes and this process is repeated until each box has guaranteed sufficient/insufficient margin, or is small enough to be neglected.…”