Advanced H∞ Control: Towards Nonsmooth Theory and - download pdf or read online
By Yury V. Orlov, Luis T. Aguilar
This compact monograph is targeted on disturbance attenuation in nonsmooth dynamic platforms, constructing an H∞ procedure within the nonsmooth surroundings. just like the normal nonlinear H∞ approach, the proposed nonsmooth layout promises either the inner asymptotic balance of a nominal closed-loop method and the dissipativity inequality, which states that the scale of an mistakes sign is uniformly bounded with recognize to the worst-case measurement of an exterior disturbance sign. This warrantly is accomplished through developing an strength or garage functionality that satisfies the dissipativity inequality and is then applied as a Lyapunov functionality to make sure the interior balance requirements.
Advanced H∞ regulate is certain within the literature for its therapy of disturbance attenuation in nonsmooth platforms. It synthesizes numerous instruments, together with Hamilton–Jacobi–Isaacs partial differential inequalities in addition to Linear Matrix Inequalities. in addition to the finite-dimensional therapy, the synthesis is prolonged to infinite-dimensional surroundings, related to time-delay and allotted parameter platforms. to assist illustrate this synthesis, the ebook specializes in electromechanical functions with nonsmooth phenomena attributable to dry friction, backlash, and sampled-data measurements. certain realization is dedicated to implementation issues.
Requiring familiarity with nonlinear platforms thought, this e-book might be obtainable to graduate scholars drawn to structures research and layout, and is a great addition to the literature for researchers and practitioners in those areas.
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Additional info for Advanced H∞ Control: Towards Nonsmooth Theory and Applications
The detailed proof of the sufficiency is similar to that of Theorem 4 and is left to the reader. 24). 27) is exponentially stable. 30) is exponentially stable. The following result, extracted from [33, 137], is in order. Theorem 13. A4/. T 2/, coupled together, are satisfied. 31) yields a T -periodic solution to the problem in question. 32) with some " > 0. 28) and some " > 0. Theorem 14. A4/. T 2/, coupled together, are satisfied. 34) yields a T -periodic solution to the problem in question. Proof.
20) t where ˚. 12), which, under the lemma conditions, satisfies the inequality k˚. ; t/k Ä me . 21) 3 Linear H1 Control of Time-Varying Systems 48 for all t and some positive m and . 0; t/ C ˚ T . ; t/S. /˚. 19) is uniformly bounded iff these solutions have the same initial conditions. 0; t/qk Ä Kme t ! 0 as t ! 1. 19). t/ is positive definite. , [78, p. t/ for each " > 0 small enough. i i / ! i i i / is thus established. i i i / ! i /. t/ is chosen with sufficiently small " > 0, and the rest of the proof follows the same line of reasoning as that used in the proof of Theorem 4.
Necessity is demonstrated based on a periodic version of the strict bounded real lemma. Let the H1 suboptimal control problem possess a solution. 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].
Advanced H∞ Control: Towards Nonsmooth Theory and Applications by Yury V. Orlov, Luis T. Aguilar