On Linear Time Invariant Systems Analysis via A Single Trajectory: A Linear Programming Approach

Hassan Abdelraouf, Fahad Albalawi, Eric Feron

Research output: Chapter in Book/Report/Conference proceedingConference contribution


In this note, a novel methodology that can extract a number of analysis results for linear time-invariant systems (LTI) given only a single trajectory of the considered system is proposed. The superiority of the proposed technique relies on the fact that it provides an automatic and formal way to obtain a valuable information about the controlled system by only having access to a single trajectory over a finite period of time (i.e., the system dynamics is assumed to be unknown). At first, we characterize the stability region of LTI systems given only a single trajectory dataset by constructing the associated Lyapunov function of the system. The Lyapunov function is found by formulating and solving a linear programming (LP) problem. Then, we extend the same methodology to a variety of essential analysis results for LTI systems such as deriving bounds on the output energy, deriving bounds on output peak, deriving L2 and RMS gains. To illustrate the efficacy of the proposed data-driven paradigm, a comparison analysis between the learned LTI system metrics and the true ones is provided.
Original languageEnglish (US)
Title of host publication2022 IEEE Conference on Control Technology and Applications (CCTA)
StatePublished - Aug 23 2022

Bibliographical note

KAUST Repository Item: Exported on 2022-12-16
Acknowledgements: This work was supported by King Abdullah University of Science and Technology (KAUST)


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