Class Of Positive Linear Systems Research Articles

Positive Linear Systems Consisting of $n$ Subsystems With Different Fractional Orders

A new class of positive linear systems consisting of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> subsystems with different fractional orders is introduced. Solution to the set of matrix linear differential equations with different fractional orders is derived. Necessary and sufficient conditions for the positivity of the fractional systems are established. It is shown that the linear electrical circuits composed of resistors, supercondensators, coils, and voltage (current) sources are positive systems with different fractional orders.

Positive linear systems with different fractional orders

Positive linear systems with different fractional ordersA new class of positive linear systems with different fractional orders is introduced. A solution to the set of linear differential equations with different fractional orders is derived Necessary and sufficient conditions for the positivity of the fractional systems are established. It is shown that the linear electrical circuits composed of resistors, supercondensators, coils and voltage (current) sources are positive systems with different fractional orders.

Pole-assignment for a class of positive linear systems

Positive systems are defined as systems with trajectories entirely in the non-negative orthant whenever the initial state is non-negative. The cohort-type model represents the class of positive linear systems considered here. The method and procedure for pole-assignment of the corresponding closed-loop positive system is proposed. The method is based on inverse eigenspectrum conditions developed for the class of system under consideration and on monomial similarity of non-negative matrices. The relation between controllability and pole-assignment is also studied. Numerical examples illustrating the procedure are provided.

Minimal order realizations for a class of positive linear systems

The positive realization problem for linear systems is to find, for a given transfer function, all possible realizations with a state space of minimal dimension such that the resulting system is a positive system. In this paper, discrete-time positive linear systems having the nonnegative orthant reachable from the origin in a finite time interval with nonnegative inputs, are considered and the solution of the positive realization problem for this class of systems is given.