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Advanced H∞ Control: Towards Nonsmooth Theory and by Yury V. Orlov, Luis T. Aguilar

By Yury V. Orlov, Luis T. Aguilar

This compact monograph is concentrated on disturbance attenuation in nonsmooth dynamic platforms, constructing an H method within the nonsmooth surroundings. just like the traditional nonlinear Happroach, the proposed nonsmooth layout promises either the interior asymptotic balance of a nominal closed-loop method and the dissipativity inequality, which states that the dimensions of an mistakes sign is uniformly bounded with appreciate to the worst-case dimension of an exterior disturbance sign. This warrantly is completed by means of developing an power or garage functionality that satisfies the dissipativity inequality and is then applied as a Lyapunov functionality to make sure the inner balance requirements.

Advanced H regulate is targeted within the literature for its remedy of disturbance attenuation in nonsmooth platforms. It synthesizes quite a few instruments, together with Hamilton–Jacobi–Isaacs partial differential inequalities in addition to Linear Matrix Inequalities. besides the finite-dimensional remedy, the synthesis is prolonged to infinite-dimensional environment, regarding time-delay and allotted parameter platforms. to aid illustrate this synthesis, the ebook specializes in electromechanical purposes with nonsmooth phenomena attributable to dry friction, backlash, and sampled-data measurements. unique consciousness is dedicated to implementation issues.

Requiring familiarity with nonlinear platforms idea, this e-book may be obtainable to graduate scholars attracted to platforms research and layout, and is a welcome boost to the literature for researchers and practitioners in those areas.

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Extra info for Advanced H∞ Control: Towards Nonsmooth Theory and Applications

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I / follow the same line of reasoning used in the proof of Lemma 6, and their details are therefore omitted. This completes the proof of Lemma 7. t/ are of appropriate dimensions, piecewisecontinuous, and uniformly bounded in t. 24). 24). G; K/k1 < for an a priori given disturbance attenuation level > mi n . t/ Á I inherited from the time-invariant treatment. 27) is exponentially stable. t/ such that the system xP D ŒA1 is exponentially stable. 2 Synthesis of Time-Varying Systems 51 Along with the suboptimality test, the following result, established in [100], yields a suboptimal controller that by iteration on approaches an optimal solution of the time-varying H1 control problem.

T 2/. 28) and some " > 0. T 2/. The detailed proof of the sufficiency follows the line of reasoning used in the proof of Theorem 4 and is left to the reader. Chapter 4 Nonlinear H1 Control In this chapter, the H1 (sub)optimal control problem is reformulated for an autonomous nonlinear system in terms of its L2 -induced norm. 3) for the H1 -norm extension in the time-varying setting]. An additional motivation comes from the time-domain interpretation, where the H1 norm stands for the maximum gain in the steady-state response to sinusoidal inputs.

Q; t/d 1 ˛ t ks. 7) t In turn, Z ks. Â/kd kqke m0 . t/. t/q ˛ t 1 q T qe 2m0 . t/ are T -periodic, the transition matrix ˚A . ; t/ is such that ˚A . ; t/ D ˚A . 5) proves to be T -periodic, too. t C T / D Z 1 D t 1 t CT T ˚A . ; t C T /S. /˚A . ; t C T /d T ˚A . C T; t C T /S. C T /˚A . C T; t C T /d Z 1 D t T ˚A . ; t/S. /˚A . t/; D where the integration variable substitution is thus proved. 10) C T has been applied. Lemma 5 According to [90,100], the time-varying version of the strict bounded real lemma reads as follows.

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