Control and Estimation of Piecewise Affine Systems by J. Xu and L. Xie (Auth.)

By J. Xu and L. Xie (Auth.)

As a strong software to review nonlinear platforms and hybrid platforms, piecewise affine (PWA) structures were broadly utilized to mechanical platforms. Control and Estimation of Piecewise Affine structures presents a number of study findings in relation to the regulate and estimation of PWA structures in a single unified view.

Chapters during this name speak about balance result of PWA structures, utilizing piecewise quadratic Lyapunov capabilities and piecewise homogeneous polynomial Lyapunov features. particular precious and adequate stipulations for the controllability and reachability of a category of PWA platforms are thought of in addition to controller and estimator layout equipment for PWA structures utilizing linear matrix inequality (LMI) and bilinear matrix inequality (BMI) ideas. A PWA method of a category of Takagi-Sugeno fuzzy approach is mentioned intensive. The booklet makes use of a couple of mechanical structures, corresponding to disk servo platforms to demonstrate some great benefits of the proposed methods.

  • Provides new insights on houses 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 keep an eye on layout in response to the promising SOS techniques

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One such approach is based on simulation. For example, Kantner and Dolye [26,27] show that robust simulation which maps sets to sets may be an alternative approach. However, the most widely used approaches are based on Lyapunov theory [28] , especially, the Lyapunov indirect method. The Lyapunov indirect method provides a powerful tool to study stability. Roughly speaking, the stability established by Lyapunov functions can be called as Lyapunov stability. Consider automatous (unforced) PWA system (2-4) as follows: δx(t) = Ai x(t) + ai , x ∈ Si , i ∈ I (3-3) The following lemma gives a criterion based on Lyapunov function for asymptotic stability and exponential stability.

Analysis and synthesis of switched linear control systems. Automatica, 41:181–195, 2005. 38 Piecewise affine systems [59] V. I. Utkin. Sliding mode in control and optimization. SpringerVerlag, 1992. [60] L. Wang and G. Feng. Piecewise H∞ controller design of discrete time fuzzy systems. IEEE Trans. on Systems Man and Cybernetics - Part B: Cybernetics, 34(1):682–686, Feb 2004. [61] J. Xu. L2 gain analysis of piecewise linear systems using sums of squares: A negative result. In IEEE Conference on Industrial Electronics and Applications, pages 441–446, Singapore, Jul 2012.

Other examples include batch processes, cars with automatic gear-box and cruise controller [50] , autonomous land vehicle and inverted pendulum on a cart [55] . As for discrete-time examples, a typical instance is interconnection of discrete-time linear systems and automata [56] . They can also be often found in digital control of hybrid systems. 8 – – – –      A top view of the system A saturation example with simulation 31  Control and estimation of piecewise affine systems converters [43] , direct torque control of three phase induction motors [21] , automotive robotized gearbox [3] and system biology [12] .

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