Title :
Stability Analysis With Dissipation Inequalities and Integral Quadratic Constraints
Author_Institution :
Aerosp. & Eng. Mech. Dept., Univ. of Minnesota, Minneapolis, MN, USA
Abstract :
This technical note considers the stability of a feedback connection of a known linear, time-invariant system and a perturbation. The input/output behavior of the perturbation is described by an integral quadratic constraint (IQC). IQC stability theorems can be formulated in the frequency domain or with a time-domain dissipation inequality. The two approaches are connected by a non-unique factorization of the frequency domain IQC multiplier. The factorization must satisfy two properties for the dissipation inequality to be valid. First, the factorization must ensure the time-domain IQC holds for all finite times. Second, the factorization must ensure that a related matrix inequality, when feasible, has a positive semidefinite solution. This technical note shows that a class of frequency domain IQC multipliers has a factorization satisfying these two properties. Thus the dissipation inequality test, with an appropriate factorization, can be used with no additional conservatism.
Keywords :
feedback; frequency-domain analysis; invariance; linear systems; perturbation techniques; stability; time-domain analysis; IQC stability theorems; dissipation inequalities; dissipation inequality test; feedback connection stability; frequency domain IQC multipliers; frequency domain dissipation inequality; input/output behavior; integral quadratic constraints; linear system; perturbation; stability analysis; time-domain IQC; time-domain dissipation inequality; time-invariant system; Equations; Frequency-domain analysis; Integral equations; Linear matrix inequalities; Robustness; Stability analysis; Time-domain analysis; Integral quadratic constraint (IQC); linear time-invariant (LTI);
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2014.2361004