Symbolic computation in analysis and synthesis for homogeneous multi-agent dynamical systems

This paper is concerned with symbolic computation in analysis and synthesis for multi-agent dynamical systems, where all the agents share a common linear time-invariant (LTI) system h(s). Such a system can be represented by the LTI system with generalized frequency variable φ(s) :=1/h(s). There are a very few results on the analysis and synthesis except stability test, since the system is large and more complex than the standard LTI system. Actually, most of the problems are nonconvex in general, and hence numerical computations do not work so well. Instead, appropriate use of symbolic computations may help to solve the problems. This paper treat two types of analysis problems on robustness of the system, namely H_∞-norm computation and D-stability test, and show that symbolic computation including quantifier elimination (QE) method effectively works for solving the problems.