Finite Time Estimation,Controland StabilityofContinuous,Discreteand Sampled-data Linear Systems

Abstract

The current research emphasizes on estimation of the states and the control of linear systems in finite time. The research contributions are presented mainly in three aspects with the common objective of achieving finite time. For sampled-data systems, estimation in finite time has been achieved using impulsive observers. Two type of such observers, namely current and prediction have been employed. The problem of continuous reconstruction through sampled measurements in finite time has been tackled using both current and prediction impulsive observers together. The classical output regulation problem has also been addressed for achieving regulation in finite time, in the presence of deterministic disturbances. To tackle the stochastic nature of the discrete time system, a finite horizon estimation has also been proposed in the presence of measurement noise. The use of deterministic input has been proposed to formulate the estimation in closed loop form. The recursive forms of the filter have been presented considering the finite length of measurements. Finite impulse response filter construction is selected with a distinguishing feature of built-in stability, reduced memory requirements and accelerated arithmetic processing on fixed size data. One of the novelty of this research is to encompass the alternate concept of finite time stability used in the literature, which is not related to classical or Lyapunov stability. For the continuous-time system with uncertainty, robust state feedback control law is constructed to achieve finite time stability. In particular, a sufficient condition in terms of differential linear matrix inequalities for achieving a guaranteed bound for the cost function satisfying simultaneously the finite time stable constraint is given. This condition is then exploited to design a state feedback control law which makes the closed loop system finite time stable