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On Saturated Linear State Feedback and Anti-Windup Design Using Sector-Based Conditions and Convex Hull Representations
  • Diego de S. Madeira
Diego de S. Madeira
Universidade Federal do CearĂ¡

Corresponding Author:[email protected]

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Abstract

In the field of closed-loop stabilization of linear systems under saturated state feedback, the question of whether a sector-based condition or a convex hull approach provides the largest invariant ellipsoid as an estimate of the system domain of attraction has been drawing great interest. This work presents a proof that, regardless of the system input size, fulfilling a popular sector-based condition for saturated linear feedback design, in fact, implies the feasibility of a well-known polytopic condition obtained through a convex hull representation of the saturated input, resulting in the same contractively invariant ellipsoid as a region of asymptotic stability. The converse is not true, but if the sector-based condition is applied in a sequential manner, then the same invariant ellipsoid determined by the polytopic approach can be obtained in a finite number of steps, for the same saturated linear state feedback. Indeed, this paper presents a complete characterization of those strategies in relation to each other, something that appears to be missing in literature. Those results are derived using a set of stabilizability conditions based on dissipativity theory and can be readily extended to deal with the anti-windup design problem as well.