Abstract
The numerical approximation of the μ -value is key towards the measurement of instability, stability analysis, robustness, and the performance of linear feedback systems in system theory. The MATLAB function mussv available in MATLAB Control Toolbox efficiently computes both lower and upper bounds of the μ -value. This article deals with the numerical approximations of the lower bounds of μ -values by means of low-rank ordinary differential equation (ODE)-based techniques. The numerical simulation shows that approximated lower bounds of μ -values are much tighter when compared to those obtained by the MATLAB function mussv.
Highlights
The μ-value was first introduced by J
An extensive amount of work has been done to study the linear feedback system; for instance, the linear control system on a manifold that is equivalent by means of diffeomorphism to an invariant system has been studied [3]
The results presented in this paper show that, in positive time delay systems, real and complex strong stability radii coincide and are computable with the help of simple mathematical formulations
Summary
The μ-value was first introduced by J. The small gain theorem deals with the robust stability of linear feedback systems and reflects the source of uncertainties originating from the original source of a single reference location within the loop of the system. The condition number corresponding to nominal matrices could be very large at some critical frequencies, which result in the conservation of uncertainties For such a case, the μ-value is defined in [2], which deals with both robust analysis and synthesis problems. The characterization of L1 -, L2 - and Lin f -gain for asymptotically stable positive systems are presented in terms of stability radii It is shown how the structured perturbation corresponding to stable matrices can be treated as a closed-loop system with uncertain structures.
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