Output Feedback Control For Nonlinear Nonminimum-phase Systems

In this paper,output feedback control design of nonlinear non-minimum-phase systems is studied.And we review the history and development of global output feedback stabilization for nonlinear non-minimum-phase systems.First,we revisit the work by Marino and Tomei in 2005 on global asymptotic stabilization by output feedback for a class of non-minimum-phase nonlinear systems in the so-called output feedback form.We point out that it is possible to find,using a new design method that involves no filter transformation,a globally stabilizing dynamic output feedback controller of order n,instead of n + 2(?-1),for the non-minimum phase nonlinear system under a slightly weaker condition(see Assumption 2.2)and the assumption that the nonlinear system is non-minimum-phase with respect to the original output,but minimum-phase with respect to a virtual linear output.And based on this result,the problem of disturbance rejection by output feedback is studied for a class of nonlinear systems.The disturbance signals are assumed to be sinusoidal with known frequencies but unknown amplitude and phase,and hence can be generated by a linear exosystem.Using the nonlinear regulator theory,we show how a global solution to the disturbance rejection problem can be derived for a class of non-minimum-phase nonlinear system in the so-called output feedback form,under appropriate conditions.And then,we investigate the problem of global stabilization by output feedback for a class of observable nonlinear systems.The nonlinear system has a cascade configuration that consists of a driven system,also known as the inverse dynamics,and a driving system.It is proved that although the zero dynamics may be unstable,there is an output feedback controller,globally stabilizing the nonlinear system if both the driven and driving systems have a lower-triangular form and satisfy linear growth and global Lipschitz-like conditions.A design procedure is provided for the construction of an n-dimensional dynamic output feedback compensator.Finally,global asymptotic stabilization by sampled-data output feedback is considered for a class of nonminimum-phase nonlinear systems.Under a global Lipschitz condition imposing on both zero dynamics(i.e.,the so-called driven system)and the driving system(which can be relaxed to the linear growth condition on zero dynamics),together with a lower-triangular structural form,we prove that the nonminimum-phase system is globally stabilizable by a sampled-data,dynamic output compensator that is composed of a nonlinear observer and a linear controller,both in discrete-time.This feature makes the proposed output feedback control scheme easier for digital implementation.