Finite zeros of positive linear continuous-time systems

Abstract

Abstract. The notion of finite zeros of continuous-time positive linear systems is introduced. It is shown that such zeros are real numbers. It is also shown that a square positive strictly proper or proper system of uniform rank with observability matrix of full column rank has no finite zeros. The problem of zeroing the system output for positive systems is defined. It is shown that a square positive strictly proper or proper system of uniform rank with observability matrix of full column rank has no nontrivial output-zeroing inputs. The obtained results remain valid for non-square positive systems with the first nonzero Markov parameter of full column rank.

Decoupling zeros of positive electrical circuits

“…The notion of the decoupling zeros of standard linear systems have been introduced by Rosenbrock [11,12]. The zeros of linear standard system have been addressed in [15] and zeros of positive continuous-time and discrete-time linear systems has been defined in [13,14]. The decoupling zeros of positive discrete-time linear systems has been introduced in [6].…”

Decoupling zeros of positive continuous-time linear systems

“…Examples of positive systems are industrial processes involving chemical reactors, heat exchangers and distillation columns, storage systems, compartmental systems, water and atmospheric pollution models [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. A variety of models having positive linear behavior can be found in engineering, management science, economics, social sciences, biology and medicine, etc.…”

“…The notion of decoupling zeros of standard linear systems have been introduced by Rosenbrock [15]. The zeros of linear standard discrete-time system have been addressed in [18] and zeros of positive continuous-time and discrete-time linear systems have been defined in [16,17]. The decoupling zeros of positive discrete-time linear systems have been introduced in [7].…”