Hikaru Sugata’s research while affiliated with The University of Tokyo and other places

A linear system with a generalized frequency variable denoted by G(s) is a system which is given by replacing the variable ‘s’ in the original transfer function G0(s) with a rational function ‘φ(s)’, i.e., G(s) is defined by G0(φ(s)). A class of large-scale systems with decentralized information structures such as a homogeneous multi-agent systems, which has a common agent dynamics h(s)=1/φ(s), can be represented by this form. In this paper, we investigate fundamental properties of such a class of systems in terms of controllability, observability, and stability. Specifically, we first derive necessary and sufficient conditions that guarantee controllability and observability of the system G(s) based on those of subsystems G0(s) and h(s). Then we show that the Nyquist type stability criterion can be reduced to a linear matrix inequality (LMI) feasibility problem. Finally, we apply the results to stability analysis of large-scale systems in three different fields and confirm the effectiveness of the approach as a general framework which can unify variety of results for homogeneous multi-agent dynamical systems.

A linear system with a generalized frequency variable denoted by G(s) is a system which is given by replacing transfer function's 's' variable in the original system G₀(s) with a rational function 'Phi(s)', i.e., G(s) is defined by Go(Phi(s)). A class of large-scale systems with decentralized information structures such as multi-agent systems can be represented by this form. In this paper, we investigate fundamental properties of such a system in terms of controllability, observability, and stability. Specifically, we first derive necessary and sufficient conditions that guarantee controllability and observability of the system Q(s) based on those of subsystems Go(s) and 1/Phi(s). Then we present Nyquist-type stability criterion which can be reduced to a linear matrix inequality (LMI) feasibility problem. Finally, we apply the results to stability analysis of a class of formation control and confirm the effectiveness of the approach as a general framework which can unify variety of results in the field.