On the robust stability analysis with real block structured uncertainties

Abstract

Accurate calculation of structured singular value is the key to robust stability analysis and control synthesis of a feedback system. The most commonly used tool in practice is the MATLAB Robust Control Toolbox where some upper and lower bounds of the structured singular value are calculated. Unfortunately, because of the discontinuities of the structured singular value with pure real perturbations, there is usually a large gap between the upper and the lower bounds obtained using this MATLAB toolbox when the system is subject to real parametric uncertainties. Motivated from the exact stability radius formula for unstructured real perturbations, we propose a modification of the real stability radius formula so that it can be applied to computing the stability radius with real block structured perturbations. Numerical simulations show that the proposed method can provide useful bounds when there are nontrivial real block structured uncertainties.

LFT Modeling and Robust Stability Analysis of Missiles with Uncertain Parameters

“…is the output vector, and A z , B z , C z , D z are all real matrices of dimensions culation of μ for systems with complex uncertainty is relatively easy, and the difference between r and lower bounds of μ is not too big. Nevertheless, it is hard to get good results for the robust analysis of systems with real uncertainty; the difference between the upper and lower bounds of and sometimes it is difficult to get the lower bound [11][12][13]. As μ needs to be calculated at every y point over the frequency range, the calculation burden is heavy.…”

“…Nevertheless, it is hard to get good results for the robust f systems with real uncertainty; the difference between the upper and lower bounds of times it is difficult to get the lower bound [11][12][13]. As μ needs to be calculated at every ver the frequency range, the calculation burden is heavy.…”

“…The -th n order Roesser model can be described as [14]: is the input vector, ncertainty is relatively easy, and the difference between evertheless, it is hard to get good results for the robust ; the difference between the upper and lower bounds of wer bound [11][12][13]. As μ needs to be calculated at every lculation burden is heavy.…”

Robust D-Stability Analysis of Linear Systems with Real Structured Uncertainties by the Stability Feeler

“…Skew μ is proposed in [16]. Even in recent years important results concerning real μ-analysis have been obtained in [17]- [20].…”

“…Therefore, much of the research in the structured singular value have been presented in [2]- [20]. The fundamental properties of μ are studied in [2]- [7].…”