A NONLINEAR SMALL GAIN THEOREM FOR THE ANALYSIS OF CONTROL-SYSTEMS WITH SATURATION

A nonlinear small gain theorem is presented that provides a formalism for analyzing the behavior of certain control systems that contain or utilize saturation, The theorem is used to show that an iterative proc edure can be derived for controlling systems in a general nonlinear, f eedforward form, This result, in turn, is applied to the control of: 1 ) linear systems (stable and unstable) with inputs subject to magnitud e and rate saturation and time delays; 2) the cascade of globally asym ptotically stable nonlinear systems with certain linear systems (those that are stabilizable, right invertible, and such that all of their i nvariant zeros have nonpositive real part); 3) the inverted pendulum o n a cart; and 4) the planar vertical takeoff and landing aircraft.