Input/output-to-state stability of switched systems under restricted switching

This paper deals with input/output-to-state stability (IOSS) of continuous-time switched nonlinear systems. Given a family of systems, possibly containing unstable dynamics, and a set of restrictions on admissible switches between the subsystems and admissible dwell times on the subsystems, we identify a class of switching signals that obeys these restrictions and preserves stability of the resulting switched system. The primary apparatus for our analysis is multiple Lyapunov-like functions. Input-to-state stability (ISS) and global asymptotic stability (GAS) of switched systems under pre-specified restrictions on switching signals fall as special cases of our results when no outputs (resp., also inputs) are considered.Comment: 14 pages, no figur

Paraplegic standing supported by FES-controlled ankle stiffness

The objective of this paper was to investigate whether a paraplegic subject-is able to maintain balance during standing by means of voluntary and reflex activity of the upper body while being supported by closed loop controlled ankle stiffness using FES. The knees and hips of the subject were held in extended positions by a mechanical apparatus, which restricted movement to the sagittal plane. The subject underwent several training sessions where the appropriate level of stiffness around the ankles was maintained by the mechanical apparatus. This enabled the subject to learn how to use the upper body for. balancing. After the subject gained adequate skills closed-loop FES was employed to regulate ankle stiffness, replacing the stiffness provided by the apparatus. A method to control antagonist muscle moment was implemented. In subsequent standing sessions, the subject had no difficulties in maintaining balance. When the FES, support was withheld, the ability to balance was lost