20-08-2014, 03:27 PM
Controller and Observer Design for Lipschitz Nonlinear Systems
[attachment=66802]
. INTRODUCTION
The output feedback control problem for nonlinear systems has
received, and continues to receive, considerable attention in the
literature due to its importance in many practical applications
where measurement of all the state variables is not possible. Output
feedback control design usually involves two related problems:
observer design and controller design which uses estimated state
and output as feedback. Unlike linear systems, separation principle
does not generally hold for nonlinear systems. Therefore, the
output feedback control problem for nonlinear systems is much
more challenging than stabilization using full-state feedback. It
is well known that the observer design problem for nonlinear
systems by itself is quite challenging. One has to often consider
special classes of nonlinear systems to solve the observer design
problem as well as the output feedback control problem. Due to
their practical significance, two special classes of systems that
were often considered in the literature are nonlinear systems with
a triangular structure and Lipschitz nonlinear systems
CONCLUSIONS
In this paper, we considered the full-state feedback control
problem, the observer design problem, and the output feedback
control problem for a class of Lipschitz nonlinear systems. We
proposed a linear full-state feedback controller and a nonlinear
observer and gave sufficient conditions under which exponential
stability is achieved. Generally, for nonlinear systems, stabilization
by state feedback plus observability does not imply stabilization
by output feedback, that is, separation principle usually does not
hold for nonlinear systems. However, for the class of nonlinear
systems considered in this paper, by using the proposed full-state
linear feedback controller and the proposed nonlinear observer,
we show that the separation principle holds; that is, the same gain
[attachment=66802]
. INTRODUCTION
The output feedback control problem for nonlinear systems has
received, and continues to receive, considerable attention in the
literature due to its importance in many practical applications
where measurement of all the state variables is not possible. Output
feedback control design usually involves two related problems:
observer design and controller design which uses estimated state
and output as feedback. Unlike linear systems, separation principle
does not generally hold for nonlinear systems. Therefore, the
output feedback control problem for nonlinear systems is much
more challenging than stabilization using full-state feedback. It
is well known that the observer design problem for nonlinear
systems by itself is quite challenging. One has to often consider
special classes of nonlinear systems to solve the observer design
problem as well as the output feedback control problem. Due to
their practical significance, two special classes of systems that
were often considered in the literature are nonlinear systems with
a triangular structure and Lipschitz nonlinear systems
CONCLUSIONS
In this paper, we considered the full-state feedback control
problem, the observer design problem, and the output feedback
control problem for a class of Lipschitz nonlinear systems. We
proposed a linear full-state feedback controller and a nonlinear
observer and gave sufficient conditions under which exponential
stability is achieved. Generally, for nonlinear systems, stabilization
by state feedback plus observability does not imply stabilization
by output feedback, that is, separation principle usually does not
hold for nonlinear systems. However, for the class of nonlinear
systems considered in this paper, by using the proposed full-state
linear feedback controller and the proposed nonlinear observer,
we show that the separation principle holds; that is, the same gain