Brief paper: A unified dissipativity approach for stability analysis of piecewise smooth systems

Authors:
Behzad Samadi;Luis Rodrigues
Affiliations:
Department of Electrical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran;Department of Electrical and Computer Engineering, Concordia University, Montreal, QC, H3G 1M8, Canada
Venue:
Automatica (Journal of IFAC)
Year:
2011

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Abstract

The main objective of this paper is to present a unified dissipativity approach for stability analysis of piecewise smooth (PWS) systems with continuous and discontinuous vector fields. The Filippov definition is considered for the solution of these systems. Using the concept of generalized gradients for nonsmooth functions, sufficient conditions for the stability of a PWS system are formulated based on Lyapunov theory. The importance of the proposed approach is that it does not need any a-priori information about attractive sliding modes on switching surfaces, which is in general difficult to obtain. A section on application of the main results to piecewise affine (PWA) systems followed by a section with extensive examples clearly show the usefulness of the proposed unified methodology. In particular, we present an example with a stable sliding mode where the proposed method works and previously suggested methods fail.