Communication Dans Un Congrès Année : 2020

LMI-based algorithms for input-saturated linear time-invariant plants

Résumé

The saturation nonlinearity and its sector properties perhaps provided the main inspiration for absolute stability theory and sector properties. The advent of linear matrix inequalities (LMI) and their efficient solvers, in the mid 1990s, provided fertile ground for the development of LMI-based stability/performance analysis and control design algorithms for linear time-invariant (LTI) plants subject to input saturation. The corresponding results, mainly developed in the past 20 years, started from state feedback designs in parallel to anti-windup augmentations of predefined linear controllers, combined with quadratic Lyapunov certificates ensuring global exponential stability. The peculiar nature of saturation, however, is such that no LTI plant can be globally exponentially stabilized from a bounded input, unless it is already globally exponentially stable in open loop. Due to this fact, non-global (or generalized) sector conditions were invented, which opened up important questions about the size of (suitable estimates of) the basin of attraction. The ensuing generalized (or non-global) absolute stability conditions evolved over the past 15 years into several increasingly advanced control design and performance analysis algorithms for input-saturated systems. In this talk we provide an overview of these developments, covering the notion of generalized sector conditions, highlighting the limits of global versus local designs, the use of deadzone-induced piecewise smooth Lyapunov functions, the multi-agent extensions of the results for bounded synchronization of identical linear plants, and possible approaches to robust designs in the presence of uncertain plants.

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Dates et versions

hal-04935661 , version 1 (07-02-2025)

Identifiants

  • HAL Id : hal-04935661 , version 1

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Luca Zaccarian. LMI-based algorithms for input-saturated linear time-invariant plants. XXIII Congresso Brasileiro de Automatica, Cassiano Rech; Daniel Pinheiro Bernardon, Nov 2020, Virtual Congress, Brazil. ⟨hal-04935661⟩
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