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

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

As a strong instrument to check nonlinear structures and hybrid structures, piecewise affine (PWA) structures were generally utilized to mechanical structures. Control and Estimation of Piecewise Affine structures presents numerous examine findings on the subject of 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 services and piecewise homogeneous polynomial Lyapunov services. particular beneficial and enough stipulations for the controllability and reachability of a category of PWA platforms are thought of besides controller and estimator layout tools for PWA structures utilizing linear matrix inequality (LMI) and bilinear matrix inequality (BMI) ideas. A PWA method of a category of Takagi-Sugeno fuzzy process is mentioned extensive. The booklet makes use of a couple of mechanical platforms, 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 ways for balance research and keep an eye on layout in keeping with the promising SOS techniques

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Observer-based output feedback controller design of piecewise discrete time linear systems. IEEE Trans. on Circuit and Systems I: Fundamental theory and applicatons, 50(3):446–450, 2003. [15] G. Feng. H∞ controller design of fuzzy dynamic systems based on piecewise Lyapunov functions. IEEE Trans. on Systems Man and Cybernetics - Part B: Cybernetics, 34(1):283–292, Feb 2004. [16] G. Feng. Stability analysis of discrete-time fuzzy dynamic systems based on piecewise Lyapunov functions. IEEE Trans.

Similar ideas can be found in [14,22] . The discrete-time counterpart has been studied by Feng [10] and Ferrari-Trecate et al. [11] . We will discuss PQLF and review some main results in the next sections, since PQLF is the one of main techniques used in our controller and estimator design. There are some other approaches, such as bi-quadratic functions [1] and global surface functions [12] . Bean et al. [1] convert the PWA system with polytope partitions into a parameterized system in terms of some logical variables.

2 can be unified as follows. 3. The system (3-3) is exponentially stable, if there exist (Pi = PiT , Ui 0, Wi 0, Uij 0)) such that (3-12) and pT Pij p < 0, ∀Ai p = 0 (3-23) hold, where for CPS, Pi = FiT T Fi and ∀i = j ∈ I, and for DPS, ∀(i, j) ∈ Ωd . 4. 2 is equivalent to either one of the following inequalities (1) Φij (Ai , Pi , Uij ) FiT Uij Fi − Pi − ATi Ai ATi Ai Pj − I (2) Φij (Ai , Pi , Uij , Υij , Ψi ) <0 −Pi + Wij −ΥTij + ATi Ψj −Υij + ΨTj Ai Pj − Ψj + ΨTj (3-24) <0 (3-25) for some (Pi = PiT , Uij FiT Uij Fi + ATi Υij + ΥTij Ai .

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