By J. Xu and L. Xie (Auth.)
As a robust software to review nonlinear structures and hybrid platforms, piecewise affine (PWA) platforms were commonly utilized to mechanical structures. Control and Estimation of Piecewise Affine structures presents a number of examine findings with regards to the regulate and estimation of PWA structures in a single unified view.
Chapters during this identify talk about balance result of PWA platforms, utilizing piecewise quadratic Lyapunov services and piecewise homogeneous polynomial Lyapunov capabilities. particular invaluable and adequate stipulations for the controllability and reachability of a category of PWA platforms are thought of in addition to controller and estimator layout tools for PWA structures utilizing linear matrix inequality (LMI) and bilinear matrix inequality (BMI) options. A PWA method of a category of Takagi-Sugeno fuzzy procedure is mentioned intensive. The publication makes use of a couple of mechanical platforms, resembling disk servo structures to demonstrate some great benefits of the proposed methods.
- Provides new insights on homes of PWA structures, together with balance, stabilizability, reachability and controllability
- Presents a unified framework for research and synthesis of either continuous-time and discrete-time PWA systems
- Presents novel techniques for balance research and regulate layout according to the promising SOS techniques
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45 Control and estimation of piecewise aﬃne systems Gon¸calves  presents a constructive global analysis methodology, which infers global properties of PWA systems solely by studying the behavior at switching surfaces associated. , maps from one switching surface to the next switching surface. They mainly analyze relay systems and saturation systems. This method actually is not easy to be used for analyzing general PWA systems. In  , Johansen presents a computational approach, which guarantees the uniform exponential stability, based on a griding technique using a linear inequality deﬁned pointwise.
21] T. Geyer. Low Complexity Model Predictive Control in Power Electronics and Power Systems. PhD thesis, Swiss Federal Institute of Technology (ETH), ZURICH, 2005.  P. Grieder. Eﬃcient Computation of Feedback Controllers for Constrained Systems. PhD thesis, Swiss Federal Institute of Technology (ETH), ZURICH, 2004.  T. Katayama H. , K. Takaba. Identiﬁcation of piecewise aﬃne systems based on statistical clustering technique. Automatica, 41:905 – 913, 2005. M. H. van Schuppen. A control problem for aﬃne dynamical systems on a full-dimensional polytope.
1). We will explore the vertex representation in Chapter 5. 2 Piecewise quadratic Lyapunov functions The key ideas applied here are ambilateral. Firstly, quadratic Lyapunov functions are deﬁned for each partition. Then they are combined to form a global Lyapunov function. 1. Note that (3-7) guarantees the positiveness of the Lyapunov function. (3-9) means that the Lyapunov function is decreasing in Si . (3-8) makes the Lyapunov function non-increasing during mode switching. If “=” is chosen, then the Lyapunov function is continuous; otherwise, the Lyapunov function is discontinuous.