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Analysis of Partial-ISS Property and Unification between ISS and Partial-ISS for Time-Varying Systems
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Volume 2, 2015
Issue 2 (April)
Pages: 23-29   |   Vol. 2, No. 2, April 2015   |   Follow on         
Paper in PDF Downloads: 27   Since Aug. 28, 2015 Views: 2005   Since Aug. 28, 2015
T. Binazadeh, School of Electrical and Electronic Engineering, Shiraz University of Technology, Shiraz, Iran.
The notion of input-to-state stability (ISS) provides a framework to investigate the boundedness of all state variables of a nonlinear system in the presence of bounded inputs and initial states. In this paper, the problem of partial stability that is stability with respect to only some of the state variables is considered. Since, partial stability finds applications in many engineering problems, some new concepts like partially bounded, partially ultimately bounded and partial-input-to-state stability (partial-ISS) are introduced in this paper. These concepts provide an extension of partial stability, in the presence of bounded inputs and initial states. Moreover, some sufficient Lyapunov-like conditions are derived to check the partial-ISS property for the nonlinear systems and in this regard a theorem is proposed and proofed. These conditions motivate checking the partial-ISS property by investigating a Lyapunov function (which is called partial-ISS Lyapunov function) for the given nonlinear system. Additionally, the unification between partial-ISS and ISS property for nonlinear time-varying systems is presented. Finally, two examples are given to show the way of investigate the partial-ISS property.
Partial Stability, Partially bounded, Partial-Input-to-State Stability, Partial-ISS Lyapunov Function
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