Some NP-complete problems in quadratic and nonlinear programming
Mathematical Programming: Series A and B
Nonsmooth analysis and control theory
Nonsmooth analysis and control theory
An Integral Invariance Principle for Differential Inclusions with Applications in Adaptive Control
SIAM Journal on Control and Optimization
Piecewise Linear Control Systems
Piecewise Linear Control Systems
SIAM Journal on Control and Optimization
International Journal of Systems Science - The Seventh Portuguese Conference on Automatic Control (Controlo'2006)
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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.