Robustness of transitions in switched linear systems

• A robustness problem for transitions in switched linear systems is considered in this paper. The specific problem is to estimate the size of the image when a subset of an affine subspace is mapped by an uncertain system to another affine subspace. It is assumed that the system dynamics is linear and that the uncertainty and the disturbances are characterized by integral quadratic constraints (IQC). The estimates can be obtained by solving a special affinely parameterized linear quadratic optimal control problem. The results are applied to the problem of verifying robustness of oscillations in a switched linear system. In particular, sufficient conditions are given, which ensure that there remains a periodic solution when the system is perturbed by a Lipschitz continuous nonlinearity.

Nyckelord

reachability analysis

uncertainty

LQ control

optimization

hybrid systems

quadratic constraints

stability

verification

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