LMI-based reduced-order observers for some discrete nonlinear systems

Asad Azemi, Edwin Engin Yaz

Research output: Contribution to journalConference articlepeer-review

2 Scopus citations


Stabilization of a nonlinear system by the use of state estimate feedback when the state variables are not available for measurement, has been an important research topic in control theory; [1]-[5] contain some sample results. In [1], a continuous nonlinear system is considered and Lyapunov results are employed for dynamic feedback stabilization. In [2], functional analytic techniques especially extended function space results are used in the stability analysis. [3] and [5] also use Lyapunov type arguments, whereas in [4], the results are based on extended linearization and especially eigenvalue separation property. In the present work, a reduced-order observer design is presented for a class of discrete time nonlinear systems. This is motivated by its potential use in dynamic feedback control of this class of discrete-time nonlinear systems in the presence of disturbances. These disturbances are assumed to be of finite energy type in this paper. The system model will be a generalization of the discrete counterpart of the one in [1]. We consider the LMI-based design of reduced-order observers for this model which will guarantee boundedness of a quadratic function of the estimation error or the boundedness of its energy. An example illustrating the design procedure will be provided at the conference. The following notation is employed in this paper. x∈Rn denotes an element of the n-dimensional real Euclidean space with norm ∥x∥ = (xTx)1/2 where xT is the transpose of x. For a square matrix A, A>0(A>0) means a positive (non-negative) definite A.

Original languageEnglish (US)
Pages (from-to)4808-4809
Number of pages2
JournalProceedings of the IEEE Conference on Decision and Control
StatePublished - 1997
EventProceedings of the 1997 36th IEEE Conference on Decision and Control. Part 1 (of 5) - San Diego, CA, USA
Duration: Dec 10 1997Dec 12 1997

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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