Template complex zonotopes for stability and invariant verification
Arvind S. Adimoolam, Thao Dang · 2017
Recently complex zonotopes were introduced as an extension of real zonotopes to the complex domain, which could capture the eigenstructure nearly periodic linear impulsive systems for stability verification. However, adding more generators to complex zonotopes distorts positive invariance and consequently refining complex zonotopes in a verification procedure is not easy. Therefore, in this paper we introduce a more general set representation, called template complex zonotopes, where the generators are fixed a-priori by a template, but the bounds on the absolute values of their combining coefficients, called scaling factors, are treated as variables and can be algorithmically synthesized. This flexibility in scaling factors leads to a more systematic and significantly more efficient stability verification procedures in case of template complex zonotope. Furthermore, the second contribution of this paper is an application of template complex zonotopes to verification of linear invariance properties of another class of hybrid systems, namely linear switched systems with additive disturbance. Experiments on a number of benchmark examples demonstrate that our approach gives better or competitive results, compared to the state-of-the-art methods and tools for these problems.