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 piece-wise-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.