This letter addresses L2-stability analysis of discrete-time continuous piecewise affine systems described in input-output form by linear combinations of basis piecewise affine functions. The proposed approach exploits an equivalent representation of these systems as the feedback interconnection of a linear system and a diagonal static block with repeated scalar nonlinearity. This representation enables the use of analysis results for systems with repeated nonlinearities based on integral quadratic constraints. This leads to a sufficient condition for L2-stability that can be checked via the solution of a single linear matrix inequality, whose dimension grows linearly with the number of basis piecewise affine functions defining the system. Numerical examples corroborate the proposed approach by providing a comparison with an alternative approach based on the computation of piecewise polynomial storage functions.

Bianchini, G., Paoletti, S., & Vicino, A. (2021). Linear fractional representations and L2-stability analysis of continuous piecewise affine systems. IEEE CONTROL SYSTEMS LETTERS, 5(1), 229-234 [10.1109/LCSYS.2020.3001173].

Linear fractional representations and L2-stability analysis of continuous piecewise affine systems

Bianchini, Gianni;Paoletti, Simone;Vicino, Antonio
2021

Abstract

This letter addresses L2-stability analysis of discrete-time continuous piecewise affine systems described in input-output form by linear combinations of basis piecewise affine functions. The proposed approach exploits an equivalent representation of these systems as the feedback interconnection of a linear system and a diagonal static block with repeated scalar nonlinearity. This representation enables the use of analysis results for systems with repeated nonlinearities based on integral quadratic constraints. This leads to a sufficient condition for L2-stability that can be checked via the solution of a single linear matrix inequality, whose dimension grows linearly with the number of basis piecewise affine functions defining the system. Numerical examples corroborate the proposed approach by providing a comparison with an alternative approach based on the computation of piecewise polynomial storage functions.
Bianchini, G., Paoletti, S., & Vicino, A. (2021). Linear fractional representations and L2-stability analysis of continuous piecewise affine systems. IEEE CONTROL SYSTEMS LETTERS, 5(1), 229-234 [10.1109/LCSYS.2020.3001173].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/1112173