Stability in terms of two measures of semiflows in space conv(R^n)

TL;DR

This paper investigates stability criteria for semiflows in convex subsets of R^n using two measures, including the Hausdorff metric and mixed volume-based measures, with applications to set differential equations and control systems.

Contribution

It introduces new stability conditions for semiflows in convex spaces using two measures, extending existing theories and providing practical criteria.

Findings

Established sufficient conditions for stability and practical stability.

Applied the criteria to specific semiflows, including set differential equations.

Demonstrated the effectiveness of the approach through numerous examples.

Abstract

The stability problem in terms of two measures for semiflows in space conv(R^n) was investigated. On the basis of comparison principle the obtained result is used to study the stability criteria for a certain semiflow in space conv(R^n). This semiflow, in particular, generalizes set differential equations and a set of attainability for linear control systems. The sufficient conditions of stability and practical stability of semiflow in terms of two measures was established. As measures the Hausdorff metric is considered as well as a special measures constructed on the basis of the certain mixed volumes. A significant number of examples of studying the stability for specific semiflows was given to illustrate the effectiveness of proposed approach.