Internally positive representations and stability analysis of linear delay systems with multiple time-varying delays

This chapter introduces the Internally Positive Representation of linear systems with multiple time-varying state delays. The technique, previously introduced for the undelayed case, aims at building a positive representation of systems whose dynamics is, in general, indefinite in sign. As a consequence, stability criteria for positive time-delay systems can be exploited to analyze the stability of the original system. As a result, an easy-to-check sufficient condition for the delay-independent stability is provided, that is compared with some well known conditions available in the literature

Constrained control of switched positive systems with discrete and distributed delays

This paper is concerned with constrained control of switched positive linear systems with discrete and distributed delays. Our goal is to design a nonnegative controller with a prescribed upper bound, such that the closed-loop system is positive and its state trajectory is located in a boundary whenever the initial condition is within the same boundary. In addition, we investigate the case when the state trajectory never reaches the boundary. It is shown that these problems are solvable via linear programming. Both continuous- and discrete-time cases are investigated in this paper. Finally, several illustrative examples are provided to show the validity of the proposed approach. © 2014 TCCT, CAA.postprin

Positive state-bounding observer for interval positive systems under L1 performance

In this paper, the positive observer problem is investigated for interval positive systems under the L1-induced performance. To estimate the state of positive systems, a pair of state-bounding positive observers is designed. A novel characterization is first proposed under which the augmented system is stable and satisfies the L1-induced performance. Necessary and sufficient conditions are then presented to design the observers. The results obtained in this paper are expressed in terms of linear programming problems, and can be easily solved by standard software. In the end, we present a numerical example to show the effectiveness of the derived design procedures. © 2014 TCCT, CAA.postprin

Positive Filtering with l

This paper is concerned with the positive filtering problem for discrete-time positive systems under the l1-induced performance. We aim to propose a pair of positive filters with error-bounding features to estimate the output of positive systems. A novel characterization is first constructed so that the filtering error system is asymptotically stable with a prescribed l1-induced performance. Then, necessary and sufficient conditions for the existence of required filters are presented, and the obtained results are expressed as linear programming problems. Moreover, it is pointed out that the results can be easily checked by standard software. In addition, a numerical example is given to show the effectiveness of the proposed design procedures