No abstract

Abstract-This paper proposes a three-stage procedure for parametric identification of PieceWise affine AutoRegressive eXogenous (PWARX) models. The first stage simultaneously classifies the data points and estimates the number of submodels and the corresponding parameters by solving the MIN PFS problem (Partition into a MINimum Number of Feasible Subsystems) for a suitable set of linear complementary inequalities derived from data. Second, a refinement procedure reduces misclassifications and improves parameter estimates. The third stage determines a polyhedral partition of the regressor set via two-class or multi-class linear separation techniques. As a main feature, the algorithm imposes that the identification error is bounded by a quantity δ. Such a bound is a useful tuning parameter to trade off between quality of fit and model complexity. The performance of the proposed PWA system identification procedure is demonstrated via numerical examples and on experimental data from an electronic component placement process in a pick-and-place machine.Index Terms-Nonlinear identification, piecewise affine autoregressive exogenous models, bounded error, MIN PFS problem.

This paper deals with the problem of the estimation of regions of asymptotic stability for continnons, antonomom, nonlinear systems. The first part of the work provides a comprehensive survey of the existing methods and of their applications in engineering fields. In the serond part certain topological considerations are first developed and the "trajectory reversing method" is then presented together with a theorem on which it is based. In the final part, several examples of application are reported, showing the efficiency of the proposed technique for low-order (second and third) systems. A. Zubov Methods The contributions included in this set refer to the Zubov theorem [5]-[7l which gives necessary and sufficient conditions

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In this note, robust stability of state–space models with respect to real parametric uncertainty is considered. Specifically, a new class of parameter-dependent quadratic Lyapunov functions for establishing stability of a polytope of matrices is introduced, i.e., the homogeneous polynomially parameter-dependent quadratic Lyapunov functions (HPD-QLFs). The choice of this class, which contains parameter-dependent quadratic Lyapunov functions whose dependence on the uncertain parameters is expressed as a polynomial homogeneous form, is motivated by the property that a polytope of matrices is stable if and only there exists an HPD-QLF. The main result of the note is a sufficient condition for determining the sought HPD-QLF, which amounts to solving linear matrix inequalities (LMIs) derived via the complete square matricial representation (CSMR) of homogeneous matricial forms and the Lyapunov matrix equation. Numerical examples are provided to demonstrate the effectiveness of the proposed approach