2017/04/13 by Samuel Coogan, Coogan, Samuel · 2 citations
Biochemistry, Genetics and Molecular Biology · Engineering · #Advanced Control Systems Optimization #Control and Stability of Dynamical Systems #FOS: Electrical engineering #Gene Regulatory Network Analysis #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1704.04218
openalex publication_date 2017/04/13 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
Monotone systems preserve a partial ordering of states along system\ntrajectories and are often amenable to separable Lyapunov functions that are\neither the sum or the maximum of a collection of functions of a scalar\nargument. In this paper, we consider constructing separable Lyapunov functions\nfor monotone systems that are also contractive, that is, the distance between\nany pair of trajectories exponentially decreases. The distance is defined in\nterms of a possibly state-dependent norm. When this norm is a weighted\none-norm, we obtain conditions which lead to sum-separable Lyapunov functions,\nand when this norm is a weighted infinity-norm, symmetric conditions lead to\nmax-separable Lyapunov functions. In addition, we consider two classes of\nLyapunov functions: the first class is separable along the system's state, and\nthe second class is separable along components of the system's vector field.\nThe latter case is advantageous for many practically motivated systems for\nwhich it is difficult to measure the system's state but easier to measure the\nsystem's velocity or rate of change. In addition, we present an algorithm based\non sum-of-squares programming to compute such separable Lyapunov functions. We\nprovide several examples to demonstrate our results.\n