Stabilization and $FLQ$-optimal control of conformable positive linear systems

Abstract

The positive stabilization problem for a class of fractional conformable linear systems in which the state takes non-negative values when the initial conditions are non-negative is addressed in this paper. Furthermore, the finite-horizon linear quadratic optimal control problem with non-negative state constraints ($FLQ^+$) is studied for continuous-time positive linear fractional systems. Necessary and sufficient conditions are proven so that the $FLQ$-optimal control given by the standard fractional inear quadratic problem is also optimal for $FLQ^+$. Then, sufficient conditions are established for the positivity of the $FLQ$-optimal closed-loop system.