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2. Guaranteed Output Bounds Using Performance Integral Quadratic Constraints

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3. Backward Reachability Using Integral Quadratic Constraints for Uncertain Nonlinear Systems

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4. Robustness analysis of uncertain time‐varying systems using integral quadratic constraints with time‐varying multipliers

   https://doi.org/10.1002/rnc.5299  

   Fry, J. Micah ; Abou Jaoude, Dany ; Farhood, Mazen ( December 2020 , International Journal of Robust and Nonlinear Control)

   This article presents a dissipativity approach for robustness analysis using the framework of integral quadratic constraints (IQCs). The derived results apply for linear time‐varying nominal systems with uncertain initial conditions. IQC multipliers are used to describe the sets of allowable uncertainty operators, and signal IQC multipliers are used to describe the sets of allowable disturbance signals. The novel concepts of dichotomic nodes and their corresponding factorizations are introduced, which allow for the aforementioned multipliers to be general time‐varying operators. The results are illustrated via the robustness analysis of a flight controller for an unmanned aircraft system tasked to perform a Split‐S maneuver.

    

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5. Integral Quadratic Constraints with Infinite-Dimensional Channels

   https://doi.org/10.23919/ACC55779.2023.10156335  

   Talitckii, Aleksandr ; Seiler, Peter ; Peet, Matthew M. ( May 2023 , Proceedings of the American Control Conference)

   Modern control theory provides us with a spectrum of methods for studying the interconnection of dynamic systems using input-output properties of the interconnected subsystems. Perhaps the most advanced framework for such inputoutput analysis is the use of Integral Quadratic Constraints (IQCs), which considers the interconnection of a nominal linear system with an unmodelled nonlinear or uncertain subsystem with known input-output properties. Although these methods are widely used for Ordinary Differential Equations (ODEs), there have been fewer attempts to extend IQCs to infinitedimensional systems. In this paper, we present an IQC-based framework for Partial Differential Equations (PDEs) and Delay Differential Equations (DDEs). First, we introduce infinitedimensional signal spaces, operators, and feedback interconnections. Next, in the main result, we propose a formulation of hard IQC-based input-output stability conditions, allowing for infinite-dimensional multipliers. We then show how to test hard IQC conditions with infinite-dimensional multipliers on a nominal linear PDE or DDE system via the Partial Integral Equation (PIE) state-space representation using a sufficient version of the Kalman-Yakubovich-Popov lemma (KYP). The results are then illustrated using four example problems with uncertainty and nonlinearity. 

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