Abstract
This paper investigates robust simultaneous stabilization (RSS) control method for two port-controlled Hamiltonian (PCH) systems and proposes results on the design of simultaneous stabilization controller with parameters for such systems. Firstly, two PCH systems are studied. Using the dissipative Hamiltonian structural properties, the systems are combined to generate an augmented PCH system. When there are external disturbances in the systems, a robust controller with parameters is designed for the systems. Secondly, an algorithm for solving parameters of the controller is proposed with symbolic computation. Finally, an illustrative example is presented to show that the RSS controller obtained in this paper works very well.
Highlights
In recent years, port-controlled Hamiltonian (PCH) systems have been extensively studied in [1,2,3,4,5,6]
We investigate RSS problem for two PCH systems and present a novel, straightforward, and convenient method to design a controller with parameters to insure that two PCH systems are simultaneous stabilization
We have investigated the RSS problem for two PCH systems and proposed a RSS controller with parameters design method
Summary
Port-controlled Hamiltonian (PCH) systems have been extensively studied in [1,2,3,4,5,6]. The Hamiltonian function in PCH systems is considered as the total energy (sum of potential energy and kinetic energy) in mechanical systems and is good candidate of Lyapunov functions for many physical systems Due to this and its nice structural properties, PCH systems have drawn a good deal of attention in practical control designs. The problem is concerned with designing a single controller which can stabilize all the systems simultaneously. Sun and Wang [18] studied simultaneous stabilization of a class of nonlinear descriptor systems via the Hamiltonian function method and proposed two new results. How to find a method for designing controller with parameters to solve RSS problem for two PCH systems is a challenging issue. We investigate RSS problem for two PCH systems and present a novel, straightforward, and convenient method to design a controller with parameters to insure that two PCH systems are simultaneous stabilization.
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