Positive Systems and Filtering Under Positivity Constraints

Abstract

Positive systems are systems whose state variables and outputs are always non-negative whenever the initial state and inputs are non-negative. These systems are frequently encountered in various fields such as biomedicine, pharmacokinetics, chemical reactions, industrial engineering, social science and economics. For this reason, there have been a lot of research interests in the analysis and synthesis of positive systems. In this talk, we will first present several examples to illustrate the use of positive systems. Then our attention will be focused on the positive filtering problem for positive linear systems. Based on a ‘system augmentation’ formulation, necessary and sufficient conditions will be proposed for the existence of a positive filter under the H∞ filtering performance. By making use of the monotonicity of the matrix inequality condition characterising the solutions, a convergent iterative linear matrix inequality algorithm will then be developed for computing a desired positive filter. The method will be illustrated numerically with a Leslie model application example.