Stabilization of discrete-time state-affine nonlinear systems by small constant controls

This paper presents an approach to stabilizing discrete-time state-affine nonlinear systems using small, constant control inputs. These systems, prevalent in various engineering domains, are linear with respect to state variables but nonlinear in parameters. This paper addresses the challenge of system stabilization when state observability is not available and when control is strongly constrained, proposing an openloop control strategy and providing necessary and sufficient conditions for global stability. The open-loop control laws ensure global asymptotic stability for homogeneous state-affine nonlinear systems and global stability for general system forms, even when single constant control fails to stabilize. This paper concludes with a numerical example that validates the stabilization results, demonstrating the system’s convergence to equilibrium with minimal control efforts.