New absolute stability criteria for robust stability and performance with locally slope-restricted monotonic nonlinearities

Absolute stability criteria are presented for locally slope-restricted monotonic nonlinearities. Unlike multivariable extensions of the Popov criterion and absolute stability criteria for monotonic nonlinearities, which only consider decoupled nonlinearities, a fully coupled nonlinearity structure is allowed. In the present work, the stability multipliers involve the para-Hermitian conjugate of the linear part of the system. In addition, a new Lur´e-Postnikov Lyapunov function is constructed for an extended Popov criterion with locally slope-restricted monotonic nonlinearities. The robust stability and performance analysis problems for real parametric uncertainty are considered. Using a parameter-dependent Lyapunov function framework for linear uncertainty, explicit connections are made between absolute stability theory and robust stability and H₂ performance