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• W1999012891 abstract "Abstract The classical definition of dissipativity for Linear Time Invariant differential (LTI) systems requires non-negativity of the net power absorbed over all system trajectories of compact support. This definition forces one to deal with only controllable systems. The more general definition uses the existence of an internal storage function as the required condition for dissipativity. While this definition allows considering uncontrollable systems also, the existential aspect of the definition raises questions about what systems admit a storage function. In this paper we provide conditions on an LTI system under which a storage function exists. Further, we also prove that this storage function is a state function , meaning the storage of energy requires no more variables than those that have to satisfy constraints for impulse-free concatenability of system trajectories. While such results have been proved for controllable systems or for a special class of uncontrollable systems, we use techniques from indefinite linear algebra to strengthen past results. The proofs of the main results above requires new results in Algebraic Riccati Equation (ARE) solvability in the context of uncontrollable state space systems: these ARE solvability results are also stated and proved in this paper." @default.
• W1999012891 created "2016-06-24" @default.
• W1999012891 creator A5004471796 @default.
• W1999012891 creator A5052006866 @default.
• W1999012891 date "2011-01-01" @default.
• W1999012891 modified "2023-09-26" @default.
• W1999012891 title "Uncontrollable dissipative dynamical systems" @default.
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• W1999012891 doi "https://doi.org/10.3182/20110828-6-it-1002.01862" @default.
• W1999012891 hasPublicationYear "2011" @default.
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