Dynamic output-feedback design for generalized Lyapunov inequalities
Abstract
Recently, properties like k-contraction and dominance analysis have proved to be valuable methods for analyzing partially stable behaviors, including multi-stability, in nonlinear systems. Differential Lyapunov matrix inequalities with matrix inertia constraints have emerged as a useful tool to verify these properties. However, efficient and systematic methods for imposing matrix inertia and designing controllers that ensure the closed-loop system satisfies these inequalities remain underdeveloped. In this work, we propose matrix inequality-based solutions for system analysis and the design of linear dynamic output-feedback controllers to address this challenge. Our results focus on partially linear systems with nonlinearities satisfying a generic differential quadratic constraint, and rely on the designer's ability to impose matrix inertia on selected variables. To this end, we introduce both convex and non-convex techniques to manage the challenges posed by matrix inertia constraints, enabling their integration into the matrix inequality problem. Additionally, we show how multiple generalized Lyapunov inequalities with different inertia constraints can be solved simultaneously using bilinear matrix inequalities constructed from the previously presented linear matrix inequalities. Finally, we demonstrate the effectiveness of the newly proposed conditions by applying them within the framework of 2-contraction for extremum control under partially known non-convex optimization objectives.
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BibTeX
@misc{zoboli2026dynamic,
title = {{Dynamic output-feedback design for generalized Lyapunov inequalities}},
author = {Samuele Zoboli and Andreu Cecilia and Sophie Tarbouriech},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-04738534v2},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Dynamic output-feedback design for generalized Lyapunov inequalities
AU - Samuele Zoboli
AU - Andreu Cecilia
AU - Sophie Tarbouriech
PY - 2026
DA - 2026/10/26
PB - HAL
UR - https://hal.science/hal-04738534v2
AB - Recently, properties like k-contraction and dominance analysis have proved to be valuable methods for analyzing partially stable behaviors, including multi-stability, in nonlinear systems. Differential Lyapunov matrix inequalities with matrix inertia constraints have emerged as a useful tool to verify these properties. However, efficient and systematic methods for imposing matrix inertia and designing controllers that ensure the closed-loop system satisfies these inequalities remain underdeveloped. In this work, we propose matrix inequality-based solutions for system analysis and the design of linear dynamic output-feedback controllers to address this challenge. Our results focus on partially linear systems with nonlinearities satisfying a generic differential quadratic constraint, and rely on the designer's ability to impose matrix inertia on selected variables. To this end, we introduce both convex and non-convex techniques to manage the challenges posed by matrix inertia constraints, enabling their integration into the matrix inequality problem. Additionally, we show how multiple generalized Lyapunov inequalities with different inertia constraints can be solved simultaneously using bilinear matrix inequalities constructed from the previously presented linear matrix inequalities. Finally, we demonstrate the effectiveness of the newly proposed conditions by applying them within the framework of 2-contraction for extremum control under partially known non-convex optimization objectives.
ER -