A modified state variable diagram method for determination of positive realizations of linear continuous-time systems with delays

Abstract

A new modified state variable diagram method is proposed for determination of positive realizations of linear continuoustime systems with delays in state and input vectors. Using the method, it is possible to find a positive realization with reduced numbers of delays for a given transfer matrix. Sufficient conditions for the existence of positive realizations of given proper transfer matrices are established. The proposed method is demonstrated on numerical examples.

Positive realizations with reduced numbers of delays for 2D continuous-discrete linear systems

“…The state variable diagram method presented in [23] for continuous-time systems with delays can be also extended to 2D continuous-discrete linear systems.…”

“…The problem of determination of the set of Metzler matrices for given stable polynomials has been formulated and partly solved in [18]. A new modified state variable diagram method for determination of positive realizations with the reduced number of delays for given proper transfer matrices of continuous-time linear systems has been proposed in [23]. An extension of this method for discrete-time linear systems is given in [24].…”

Determination of positive realizations with reduced numbers of delays or without delays for discrete-time linear systems

“…Determination of the state space equations for given transfer matrix is a classical problem, called realization problem, which has been addressed in many papers and books [1,3,16,[17][18][19][20][21][22][23]. It is well-known that [1,2,16] that to find a realization for a given transfer function first we have to find a state matrix for given denominator of the transfer function.…”

“…The problem of determination of the set of Metzler matrices for given stable polynomials has been formulated and partly solved in [19]. A new modified state variable diagram method for determination of pos-itive realizations with reduced number of delays for given proper transfer matrices of continuous-time linear systems has been proposed in [22].…”

A new approach to the realization problem for fractional discrete-time linear systems

“…The realization problem for fractional linear systems has been analyzed in [6,7,[25][26][27][28][29][30] for positive 2D hybrid linear systems in [24,31,32] and for fractional systems with delays in [33,34]. A new modified state variable diagram method for determination of positive realizations with reduced number of delays for given proper transfer matrices has been proposed in [35].…”