This paper provides a geometrical derivation of the Hybrid Minimum Principle (HMP) for autonomous impulsive hybrid systems on Riemannian manifolds, i.e. systems where the manifold valued component of the hybrid state trajectory may have a jump discontinuity when the discrete component changes value. The analysis is expressed in terms of extremal trajectories on the cotangent bundle of the manifold state space. In the case of autonomous hybrid systems, switching manifolds are defined as smooth embedded submanifolds of the state manifold and the jump function is defined as a smooth map on the switching manifold. The HMP results are obtained in the case of time invariant switching manifolds and state jumps on Riemannian manifolds.
Uniform Exponential Stability Analysis of Impulsive Linear Time-Invariant Systems on Banach and Hilbert Spaces: Non-Coercive and Coercive Stability Conditions
School of Life Sciences, University of Applied Sciences, Muttenz, Switzerland（瑞士穆滕兹应用科学大学生命科学学院）；Department of Engineering, University of Perugia, Perugia, Italy（意大利佩鲁贾大学工程学院）；Université Grenoble Alpes, CNRS, Grenoble INP, GIPSA-lab, Grenoble, France（法国格勒诺布尔阿尔卑斯大学、法国国家科学研究中心、格勒诺布尔理工学院、GIPSA实验室）
Optimal Impulse Control of SIR Epidemics over Scale-Free Networks
St. Petersburg State University（圣彼得堡国立大学）；Department of Electrical and Computer Engineering, Tandon School of Engineering, New York University（纽约大学坦登工程学院电气与计算机工程系）
