Discrete-time extensions of mixed-μ bounds to monotonic and odd monotonic nonlinearities

Using the parameter-dependent Lyapunov function framework of Haddad and Bernstein this paper extends and connects some of the classical absolute stability results on discrete-time systems with monotonic and odd monotonic feedback nonlinearities to modern robust stability and performance problems for constant real parameter uncertainty. As in the continuous-time case, it is shown that an immediate application of this framework provides a generalization and reformulation of discrete-time mixed-μ theory in terms of Lyapunov functions and Riccati equations while blending H₂ robust performance within the μ framework.