”2/H∞ based sliding mode control: A partial eigenstructure assignment method

This paper is devoted to the problem of designing a sliding surface for an underlying system, while H2/H∞ performance specifications of the closed-loop system are under control. This scheme is different from a large number of the existing methods in the literature for the sliding surface design, in the sense that it will penalize the required level of control effort to maintain sliding. This novel scheme consists of two stages. First, exploiting a certain partial eigenstructure assignment method, a state feedback gain is selected that ensures precise locations for some of the closed-loop system poles while minimizing the H∞-norm (H2-norm) of a specific closed-loop transfer function and satisfying an H2-norm (H∞-norm) constraint on the same or another closed-loop transfer function. Following this, the second stage derives the sliding surface and thereby the control law associated with the particular state feedback designed in the first stage by using one of an approach developed for this purpose. We present a numerical example to demonstrate the remarkable performance of the proposed scheme.

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