Fixed-architecture controller synthesis for systems with input-output time-varying nonlinearities

Develops a fixed-architecture controller analysis and synthesis framework that addresses the problem of multivariable linear time-invariant systems subject to plant input and output nonlinearities while accounting for robust stability and robust performance over the allowable class of nonlinearities. The proposed framework is based on the classical Lur´e problem and related Aizerman conjecture concerning the stability of a feedback loop involving a sector-bounded nonlinearity. Specifically, the authors extend the classical notions of absolute stability theory to guarantee closed-loop stability of multivariable systems in the presence of input nonlinearities. In order to capture closed-loop system performance the authors also consider the minimization of a quadratic performance criterion over the allowable class of input nonlinearities. The principal result is a set of constructive sufficient conditions for absolute stabilization characterized via a coupled system of algebraic Riccati and Lyapunov equations