Abstract
The problem of decentralized impulse controllability/observability for large-scale interconnected descriptor systems with two subsystems by derivative feedback is studied. Necessary conditions for the existence of a derivative feedback controller for the first subsystem of the large-scale interconnected descriptor systems ensuring the second subsystem to be impulse controllable and impulse observable are derived, respectively. Based on the results, a derivative feedback controller for the first subsystem of the large-scale interconnected descriptor systems is constructed easily such that the second subsystem is impulse controllable or impulse observable. Finally, examples are given to illustrate the effectiveness of the results obtained in this paper.
Highlights
Descriptor systems are referred to as singular systems, implicit systems, differential algebraic systems, semistate systems, or generalized state space systems
The control of descriptor systems has been extensively studied in past years and a great number of results based on the theory of standard state space systems have been generalized to descriptor systems [1,2,3,4,5]
It is pointed out in the work [6] that the necessary and sufficient condition for impulse elimination via proportional state feedback is that the considered system is impulse controllable
Summary
Descriptor systems are referred to as singular systems, implicit systems, differential algebraic systems, semistate systems, or generalized state space systems. It is important to study the problem of eliminating impulsive behavior of a descriptor systems via certain feedback controllers. It is pointed out in the work [6] that the necessary and sufficient condition for impulse elimination via proportional state feedback is that the considered system is impulse controllable. Mathematical Problems in Engineering is necessary and sufficient for the existence of impulsive mode eliminating proportional state feedback controller. To the best of our knowledge, the research on decentralized impulse controllability/observability of interconnected descriptor systems still receives little attention. We study the problem of decentralized impulsive controllability/observability for interconnected descriptor systems. The impulse controllability/observability problem of descriptor systems involves the rank constraints of matrix pencil with parameter K.
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