Discrete time adaptive control of linear dynamic systems with a two-segment piecewise-linear asymmetric nonlinearity

In this note a method is presented for doing discrete adaptive control of a nonlinear system which is given by a cascade connection of a "two-segment piecewise-linear asymmetric nonlinearity" followed by a linear system. A switching gain sequence is introduced to make the parameter identification time invariant. The algorithm will ensure that the closed-loop system is globally convergent and stable for both the deterministic and stochastic cases.