Internally stable nonlinear systems with disturbances: a parameterization

Abstract

This paper deals with the control of a nonlinear system whose output is subjected to an additive disturbance. The main result is a simple parameterization of the set of all system responses that can be obtained through internally stable control of the given system. The parameterization provides a clear indication of the effects of the disturbance on the response of the stabilized closed loop system. The class of achievable responses is determined by the ''numerator'' of a right coprime fraction representation of the system being controlled. Here, u E S (Rm) is the input sequence, y E S (RP) is the output sequence, and x E S(Rn) is an intermediate sequence of "states." In case the functions f :Rn x Rm-+ Rn and h:Rn-+ RP are continuous, then (2.1) constitutes a continuous realiz,ation of the system :E. A system M:S(Rm)-+ S(Rm) is bicausal if it is causal and if it possesses a causal inver$e. It can be readily shown that the composition of two bicausal systems is bicausal. Likewise, the composition of two causal systems is causal, and the composition of a causal system with a strictly causal one is i. ! .

A Performance Bound for a Nonlinear Control System

“…The presentation is for discrete-time time-invariant nonlinear systems. Almost all the necessary mathematics is contained in [2] and [3].…”

A simple approach to nonlinear state feedback design

“…Alternative approaches to the control of nonlinear systems can be found in [11], [12], [5], [6], [18], [3], [17], [7], [2], [14], [16], [19], [15], [8], [1], [4], [13] and [9], in the references cited in these publications, and elsewhere.…”

“…The static state feedback controllers derived here can be utilized to obtain a fraction representation of Σ; using such a fraction representation, one can derive dynamical state feedback controllers that assign desirable dynamics to the closed loop system ( [5], [6], [7], [8]). …”