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| We analyze the concept of dissipativity in the sense of Willems for nonautonomous linear-quadratic (LQ) control systems. A nonautonomous system of Hamiltonian ODEs is associated with such an LQ system by way of the Pontryagin Maximum Principle. The concepts of exponential dichotomy and weak disconjugacy for this Hamiltonian ODE are related to that of dissipativity for the LQ system in order to investigate the relationship between the strict dissipativity condition and the conditions arising in the frequency theorem. We also investigate LQ systems which are dissipative but not strictly so. We find sufficient conditions for the existence of a storage function and of a stabilizing feedback control. And we see that the concept of weak disconjugacy can be used to formulate such conditions.
The work is based on previous results obtained in collaboration with Roberta Fabbri, Sylvia Novo and Rafael Obaya. |
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