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Advances in H∞ Control Theory pp 43–59Cite as

Robust Control of Linear Systems via Switching

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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 481))

Abstract

An alternative approach to robust control is presented where the uncertainty polytope is divided into overlapping smaller regions and where each of these regions is assigned to a separate subsystem. Assuming that there is an online information on which of the regions the parameters of the system move to, the method of the previous chapters for \(H_{\infty }\)  design of switched system with dwell time is applied. In order to handle the switching between the subsystems, a Lyapunov Function (LF) in a quadratic form, which is nonincreasing at the switching instances, is assigned to each subsystem. This function is used to determine the stability and to find a bound on the \({L}_2\)-gain of the switched system. The obtained results are then used to solve the corresponding robust \(H_{\infty }\)  state-feedback and static output-feedback control problems. Two practical examples are given which show that, by deliberately introducing switching, the obtained designs are less conservative than those achieved by the available standard techniques.

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Author information

Authors and Affiliations

  1. Department of Electrical and Electronics Engineering, Holon Institute of Technology, Holon, Israel

    Eli Gershon

  2. School of Electrical Engineering, Tel Aviv University, Tel Aviv, Israel

    Uri Shaked

Authors
  1. Eli Gershon
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  2. Uri Shaked
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Correspondence to Eli Gershon .

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Gershon, E., Shaked, U. (2019). Robust Control of Linear Systems via Switching. In: Advances in H∞ Control Theory. Lecture Notes in Control and Information Sciences, vol 481. Springer, Cham. https://doi.org/10.1007/978-3-030-16008-1_4

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