Ultimate Bounds and Robust Invariant Sets for Linear Systems with State-Dependent Disturbances

Sorin Olaru 1, 2, 3 Vasso Reppa 1, 2
1 L2S - Laboratoire des signaux et systèmes
2 CentraleSupélec
3 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France
Abstract : The objective of this chapter is to present a methodology for computing robust positively invariant sets for linear, discrete time-invariant systems that are affected by additive disturbances, with the particularity that these disturbances are subject to state-dependent bounds. The proposed methodology requires less restrictive assumptions compared to similar established techniques, while it provides the framework for determining the state-dependent (parameterized) ultimate bounds for several classes of disturbances. The added value of the proposed approach is illustrated by an optimization-based problem for detecting the mode of functioning of a switching system.
Keywords : State dependent disturbances Ultimate bounds Invariant sets
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Sorin Olaru, Vasso Reppa. Ultimate Bounds and Robust Invariant Sets for Linear Systems with State-Dependent Disturbances. Sorin Olaru, Alexandra Grancharova, Fernando Lobo Pereira. Developments in Model-Based Optimization and Control, 464, Springer, pp.339-359, 2015, Lecture Notes in Control and Information Sciences, 9783319266855. ⟨10.1007/978-3-319-26687-9_16⟩. ⟨hal-01260190⟩

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