An Amendment to "Control Contraction Metrics: Convex and Intrinsic\n Criteria for Nonlinear Feedback Design"

2017/11/21 by Ian R. Manchester, Manchester, Ian R., Thomas Chaffey +1
Engineering · #Advanced Control Systems Optimization #Control Systems and Identification #Control and Stability of Dynamical Systems #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.1711.08128

openalex publication_date 2017/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide an amendment to the first theorem of "Control Contraction Metrics:\nConvex and Intrinsic Criteria for Nonlinear Feedback Design" by Manchester &\nSlotine in the form of an additional technical condition required to show\nintegrability of differential control signals. This technical condition is\nshown to be satisfied under the original assumptions if the input matrix is\nconstant rank, and also if the strong conditions for a CCM hold. However a\nsimple counterexample shows that if the input matrix drops rank, then the\nweaker conditions of the original theorem may not imply stabilizability of all\ntrajectories. The remaining claims and illustrative examples of the paper are\nshown to remain valid with the new condition.\n

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