State for linear time-varying systems, with applications to dissipative systems
State for linear time-varying systems, with applications to dissipative systems
An intrinsic definition of state is given for systems described by higher-order linear differential equations with time-varying coefficients. Based on this definition we characterize a polynomial differential operator that acting on a system trajectory defines a corresponding state one, and we illustrate a procedure to compute a state variable from the differential equations. We prove that there exist representations of first order in such state variable and zeroth order in the input and output variables. We also consider linear, time-varying dissipative systems, and we give several characterisations of the property of cyclo-losslessness. We prove that for dissipative systems the storage function is a quadratic function of the state.
State variable, differential-algebraic equations with time-varying coefficients, dissipativity, storage function, bilinear and quadratic differential forms
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b
Rapisarda, Paolo
(2021)
State for linear time-varying systems, with applications to dissipative systems.
SIAM Journal of Control and Optimization.
(In Press)
Abstract
An intrinsic definition of state is given for systems described by higher-order linear differential equations with time-varying coefficients. Based on this definition we characterize a polynomial differential operator that acting on a system trajectory defines a corresponding state one, and we illustrate a procedure to compute a state variable from the differential equations. We prove that there exist representations of first order in such state variable and zeroth order in the input and output variables. We also consider linear, time-varying dissipative systems, and we give several characterisations of the property of cyclo-losslessness. We prove that for dissipative systems the storage function is a quadratic function of the state.
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StateMapsSIAMFinal
- Accepted Manuscript
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Accepted/In Press date: 8 October 2021
Keywords:
State variable, differential-algebraic equations with time-varying coefficients, dissipativity, storage function, bilinear and quadratic differential forms
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Local EPrints ID: 451960
URI: http://eprints.soton.ac.uk/id/eprint/451960
PURE UUID: a0330a59-db4c-48d6-8f62-bd561f90f986
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Date deposited: 04 Nov 2021 17:33
Last modified: 16 Mar 2024 14:19
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Author:
Paolo Rapisarda
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