Positive State-bounding Observer For Positive Interval Continuous-time Systems

Along with wide application of continuous-time interval systems,which causing the attention of cybernetic researchers,the stability and the controllers design problems of the systems have been widely investigates. While in practice often requires the state of the systems to satisfy the nonnegative,which prompt the research turn to systems of positive exploration and study. However, the positivity of the state variables will take many new issues, which cannot be solved in general by applying well-established methods for general systems. for example,the observer for general systems may not be applicable to the positive systems, for the state estimates may escape form the nonnegative quadrant in some time interval,which in turn implies that the estimation is not valid. So,the observer should be designed in such situation that the state is nonnegative, like the system state itself. This paper analyzes the sign problems of positive state-bounding observer for these two types of the linear and nonlinear positive continuous-time interval systems. The main works are given as follows:1The design problem of positive state-bounding observer for positive continuous time interval linear systems. First due to the positivity requirement on the observes,a pair of positive observers is proposed to estimate the state of positive systems at all times can be given,then analysis the stability conditions of the systems, and the desired observer matrices can be constructed easily through the solutions of linear matrix inequalities(LMIs).Finally, a illustrative example is provided to show the effectiveness and applicability of the theoretical results.2The design problem of positive state-bounding observer for positive continuous time interval nonlinear systems.lt can take a nonlinear system into a linear combination of several linear subsystems by the T-S fuzzy model.By using the Lyapunov stability,a sufficient condition of the symptotic stability for positive interval continuous-time fuzzy systems is given.A pair of positive state-bounding observers is proposed to estimate the state of systems,a sufficient condition for the existence of desired observers is given and to be proved.At last,a numerical example is given to show the effectiveness of the proposed method. Figure [amount] table [amount] reference [amount]...