Incremental Stability for Complex Nonlinear Systems

The notion of incremental stability focuses on the convergence of trajectories with respect to each other rather than with respect to an equilibrium point or a fixed trajectory. Considering the advantages of incremental stability property in the construction of symbolic models, our research focuses on providing sufficient conditions and design control strategies enforcing incremental stability property for complex control systems.

Highlight of the proposed results include:

1. We proposed a coordinate invariant notion of incremental stability for stochastic control systems.
2. We proposed a backstepping controller design for stochastic Hamiltonian systems with jumps.
3. We introduce a notion of incremental stability for retarded jump-diffusion systems and provide sufficient conditions for it in terms of the existence of a notion of incremental Lyapunov functions.