From feedback to cascade-interconnected systems: Breaking the loop

The purpose of this paper is to observe that a feedback interconnection is equivalent to a cascaded inter-connection ¿if you twist your eyes¿. We establish conditions under which a feedback interconnected (time-invariant or non-autonomous) system can be regarded as a cascaded time-varying system. The ¿technique¿ finds motivation in numerous particular applications, notably, in output feedback (observer-based) control where two subsystems are feedback interconnected and it results desirable to analyze the system as a cascade. Indeed, cascaded-based design allows for considerably simple controllers that exploit the physical structure of the system and sufficient conditions for stability of cascaded systems are often easier to apply than finding strict Lyapunov functions. As an illustration of how to use our main results we revisit a recently published article on a problem that, to the best of our knowledge, remains open for many years: to establish uniform global asymptotic stability of the closed-loop system for robot manipulators via (dynamic) position feedback.