MingQing Xiao

Nonlinear Observer Design in the Siegel Domain

We extend the method of Kazantzis and Kravaris [Systems Control Lett., 34 (1998), pp. 241--247] for the design of an observer to a larger class of nonlinear systems. The extended method is applicable to any real analytic observable nonlinear system. It is based on the solution of a first-order, singular, nonlinear PDE. This solution yields a change of state coordinates which linearizes the error dynamics. Under very general conditions, the existence and uniqueness of the solution is proved. Lyapunovs auxiliary theorem and Siegels theorem are obtained as corollaries. The technique is constructive and yields a method for constructing approximate solutions.

Observers for linearly unobservable nonlinear systems

We provide a method for constructing local observers for some nonlinear systems around a critical point where the linearization is not observable or not detectable. Two examples are provided to illustrate the results of the paper.

Nonlinear discrete-time observer design with linearizable error dynamics

A necessary and sufficient condition for the existence of a discrete-time nonlinear observer with linearizable error dynamics is provided. The result can be applied to any real analytic nonlinear system whose linear part is observable. The necessary and sufficient condition is the solvability of a nonlinear functional equation. Furthermore, the well-known Siegels theorem on the linearizability of a mapping is naturally reproduced in a corollary. The proposed observer design method is constructive and can be applied approximately to any sufficiently smooth, linearly observable system yielding a local observer with approximately linear error dynamics.

A direct method for the construction of nonlinear discrete-time observer with linearizable error dynamics

We provide a direct method for the design of nonlinear discrete-time observers by a construction of a change of variables. An explicit expression of the change of variables is given. Some simulations for chaotic systems, such as Lozi system and He/spl acute/non system, are provided to illustrate the proposed method.

Erratum: Nonlinear Observer Design in the Siegel Domain

There is an error in the proof of the main result of our paper SIAM J. Control Optim., 41 (2002), pp. 932--953]. An additional assumption is needed for the main result to hold. In this erratum, we supply a corrected version of the main result.

Almost Sure Stability of Discrete-Time Switched Linear Systems: A Topological Point of View

In this paper, we study the stability of discrete-time switched linear systems via symbolic topology formulation and the multiplicative ergodic theorem. A sufficient and necessary condition for

The global existence of nonlinear observers with linear error dynamics: A topological point of view

\mu_A

Center Manifold of the Viscous Moore--Greitzer PDE Model

-almost sure stability is derived, where

A Survey of Observers for Nonlinear Dynamical Systems

\mu_A

Nonlinear Observer Design in the Siegel Domain Through Coordinate Changes 1

is the Parry measure of the topological Markov chain with a prescribed transition (0,1)-matrix