Weak Input-to-State Stability Properties for Navigation Function Based Controllers

Due to topological constraints, navigation functions, are not, except from trivial cases, equivalent to quadratic Lyapunov functions, hence systems based on navigation functions cannot directly accept an input-to-state stability (ISS) characterization. However a relaxed version of input-to-state stability, namely almost global ISS (aISS), is shown to be applicable. The proposed framework provides compositional capability for navigation function based systems. Cascade as well as feedback interconnections of aISS navigation systems are shown to also possess the aISS property under certain assumptions on the interconnections. Several simulated examples of navigation systems are presented to demonstrate the effectiveness of the proposed scheme