Enforcing negative imaginary dynamics on mathematical system models

Descriptor systems state-space conditions to guarantee negative imaginary properties without minimality restrictions

“…Many valuable theoretical results have been developed for negative imaginary systems. For instance, the concept of negative imaginary systems has been refined in [6]- [9]; the negative imaginary lemmas for standard linear systems have been developed in [6], [7], [10]; applications of negative imaginary theory can be found in [3], [5], [11]. On the other hand, descriptor systems provide a suitable model for mechanical systems and circuit systems [12], [13].…”

Forward action to make a system negative imaginary

“…Along the same line of the research discussed in our paper, Mabrok and co-workers [12] showed how to enforce the negative imaginary dynamics via perturbations of a non-negative imaginary state-space realization and Song and co-workers [13] through the use of a static feedback of the form u = Kx. Our approach complements these results and shows another technique to enforce this property.…”

“…In addition, our technique is only based on the input-output model of the system. The paper [12] also points out another important motivation for the search of methods to make a system negative imaginary. In fact, in the problem of the identification of a model of a physical system, which is known to be negative imaginary, some identification techniques may yield a representation for which this property is not guaranteed.…”

“…In fact, in the problem of the identification of a model of a physical system, which is known to be negative imaginary, some identification techniques may yield a representation for which this property is not guaranteed. Techniques based on the perturbation of the state-space matrices as in [12], on feedback of the state variables as in [13], or on the addition of a low order, low gain transfer function matrix as in our paper can be helpful in solving this problem.…”

LMI based robust state feedback control of negative-imaginary systems

“…The concept of negative imaginary system was first introduced in [1,2] and subsequently, several research works have been explored to develop analysis and synthesis frameworks for negative imaginary (NI) systems [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Negative imaginary systems are important in engineering practice as this class of system appears quite often in practical problems, for example, when considering the transfer function from force actuators to collocated position sensor in lightly damped structure [1][2][3][4]6,9,[14][15][16][17]19,22], from input voltage to output voltage in electrical active filter circuits [13], from input voltage to shaft rotational velocity in a DC motor [7].…”