## Abstract

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∈R^{n} denotes an element of the n-dimensional real Euclidean space with norm ∥x∥ = (x^{T}x)^{1/2} where x^{T} is the transpose of x. For a square matrix A, A>0(A>0) means a positive (non-negative) definite A.

Original language | English (US) |
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Pages (from-to) | 4808-4809 |

Number of pages | 2 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

Volume | 5 |

State | Published - 1997 |

Event | Proceedings of the 1997 36th IEEE Conference on Decision and Control. Part 1 (of 5) - San Diego, CA, USA Duration: Dec 10 1997 → Dec 12 1997 |

## All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization