preprints.org > engineering > control and systems engineering > doi: 10.20944/preprints202311.1716.v1

Preprint Technical Note Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 27 November 2023 / Approved: 27 November 2023 / Online: 27 November 2023 (14:43:07 CET)

This paper addresses a mode-dependent state-feedback H∞ control for descriptor hybrid systems, considering both the absence and presence of actuator saturation. Firstly, the necessary and sufficient conditions for the stochastic admissibility criterion with H∞ performance ? of the closed-loop system is proposed. Given the proposed non-convex condition, the author reformulates it into linear matrix inequalities (LMIs). Then, to extend the result to the systems with actuator saturation, the actuator saturated control input is expressed as a linear combination of given state-feedback control input and a virtual control input that remains under the saturation level. To verify this expression, the set invariant condition is also suggested by using the singular mode-dependent Lyapunov function candidate. Therefore, the LMI conditions for the existence of the mode-dependent state-feedback H∞ control and the ellipsoidal shape of invariant set are successfully derived. Two numerical examples demonstrate the effectiveness of the proposed approach in optimizing H∞ performance $\gamma$ and identifying the largest invariant set.

descriptor systems; hybrid systems; stochastic systems; H∞ control; input saturation; set invariant

Engineering, Control and Systems Engineering

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