Interval Observer Design for Metzlerian Takagi-Sugeno Systems

The generalized interval observer design conditions for continuous-time Metzlerian Takagi-Sugeno systems are presented in the paper. Attention is focused on the analysis and design guaranteeing the asymptotic convergence of the interval observer error and positivity of interval observer state. The relationship between the nonnegativity of the observer gains and the corresponding positive observer state attractiveness is also shown. The method presented extends and generalizes the results that recently appeared in the literature.

Positive observers for linear positive systems in a Hilbert lattice space

In this work, we investigate the question of designing a positive observer for a class of infinite dimensional linear positive systems. We present a new observer design based on a classical Luenberger-like observer. The proposed observer is positive. That is, it ensures that the state estimates are nonnegative at any time. The existence of such positive observers is proven by a specific choice of the observer gain and using positive bounded perturbation results. We show in particular that the error of the state estimation converges exponentially to zero. Finally, the main result is applied to an isothermal tubular (bio) reactor model, namely the plug-flow (bio) reactor model. The approach is illustrated by some numerical simulations.

Nonfragile observer-based guaranteed cost finite-time control of discrete-time positive impulsive switched systems

This paper considers the nonfragile observer-based guaranteed cost finite-time control of discrete-time positive impulsive switched systems(DPISS). Firstly, the positive observer and nonfragile positive observer are designed to estimate the actual state of the underlying systems, respectively. Secondly, by using the average dwell time(ADT) approach and multiple linear co-positive Lyapunov function (MLCLF), two guaranteed cost finite-time controller are designed and sufficient conditions are obtained to guarantee the corresponding closed-loop systems are guaranteed cost finite-time stability(GCFTS). Such conditions can be solved by linear programming. Finally, a numerical example is provided to show the effectiveness of the proposed method.