  Input-to-state stability (ISS) of switched systems is studied where the
individual subsystems are connected in a serial cascade configuration, and the
states are allowed to reset at switching times. An ISS Lyapunov function is
associated to each of the two blocks connected in cascade, and these functions
are used as building blocks for constructing ISS Lyapunov function for the
interconnected system. The derivative of individual Lyapunov functions may be
bounded by nonlinear decay functions, and the growth in the value of Lyapunov
function at switching times may also be a nonlinear function of the value of
other Lyapunov functions. The stability of overall hybrid system is analyzed by
constructing a newly constructed ISS-Lyapunov function and deriving lower
bounds on the average dwell-time. The particular case of linear subsystems and
quadratic Lyapunov functions is also studied. The tools are also used for
studying the observer-based feedback stabilization of a nonlinear switched
system with event-based sampling of the output and control inputs. We design
dynamic sampling algorithms based on the proposed Lyapunov functions and
analyze the stability of the resulting closed-loop system.
