Abstract
Abstract In this work-in-progress paper we propose a method of stabilizing controller synthesis for unstable linear systems with constrained control using polyhedral Lyapunov functions. Our method is based on the Frank-Wolfe algorithm for quadratic optimization, which is suitable for implementation in embedded microprocessors. The method implicitly constructs an inner approximation of polyhedral controllable set for unstable subsystem of lower dimension and then converts its boundary into polyhedral Lyapunov function without explicit construction of the associated polytope.
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