Section: New Results

Set-Theoretic Methods of Control And Estimation

In many cases due to parametric and/or signal uncertainties presented in a plant model it is not possible to design a conventional observer, which provides a point-wise estimate of state in a finite time or asymptotically. In this case it is still frequently possible to design observers, which generate an estimate on the set of the admissible values of the state at the current instant of time. The recent new results in this field are listed below:

• An interval observer for Linear Time-Varying systems is proposed in [38] . A constructive approach to obtain a time-varying change of coordinates, ensuring the cooperativity of the observer error in the new coordinates, is provided in order to simplify the design of the interval observer.

• In [58] the problem of interval observer design is addressed for a class of descriptor linear systems with delays. An interval observation for any input in the system is provided. The control input is designed together with the observer gains in order to guarantee interval estimation and stabilization simultaneously.

• The estimation problem of a system with unknown time-delay and unknown input gains is considered in [49] . The interval observation technique is applied in order to obtain guaranteed interval of the system state.

• The book [82] introduces newly developed robust control design technique for a wide class of continuous-time dynamical systems called the “attractive ellipsoid method.” It studies nonlinear affine control systems in the presence of uncertainty and presents a constructive and easily implementable control strategy that guarantees certain stability properties.