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Projection-based control (PBC) systems have significant engineering impactand receive considerable scientific attention. To properly describe closed-loopPBC systems, extensions of classical projected dynamical systems are needed,because partial projection operators and irregular constraint sets (sectors)are crucial in PBC. These two features obstruct the application of existingresults on existence and completeness of solutions. To establish a rigorousfoundation for the analysis and design of PBC, we provide essential existenceand completeness properties for this new class of discontinuous systems.

Existence and Completeness of Solutions to Extended Projected Dynamical Systems and Sector-bounded Projection-based Controllers