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Stabilizing Control for Discrete-time Singular Bilinear Systems

Qingling Zhang

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Abstract

The existing conditions of stabilizing control for discrete-time singular bilinear systems are studied and the corresponding control scheme is given.By decomposing singular systems and applying Lyapunov method,it is proved that linear state control can make the closed-loop system asymptotically stable around the origin.The related proof of such a kind of discrete-time singular bilinear systems may be regarded as the extension of the normal discrete-time bilinear system.An example show the validity of the method.The stabilizing criterion obtained has instructive value for choosing an appropriate control method.

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What this paper is about

The existing conditions of stabilizing control for discrete-time singular bilinear systems are studied and the corresponding control scheme is given.By decomposing singular systems and applying Lyapunov method,it is proved that linear state control can make the closed-loop system asymptotically stable around the origin.The related proof of such a kind of discrete-time singular bilinear systems may be regarded as the extension of the normal discrete-time bilinear system.An example show the validity of the method.The stabilizing criterion obtained has instructive value for choosing an appropriate control method.

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Available abstract

The existing conditions of stabilizing control for discrete-time singular bilinear systems are studied and the corresponding control scheme is given.By decomposing singular systems and applying Lyapunov method,it is proved that linear state control can make the closed-loop system asymptotically stable around the origin.The related proof of such a kind of discrete-time singular bilinear systems may be regarded as the extension of the normal discrete-time bilinear system.An example show the validity of the method.The stabilizing criterion obtained has instructive value for choosing an appropriate control method.

Key concepts: Mathematics, Bilinear interpolation, Discrete time and continuous time, Control theory (sociology), Singular solution, Extension (predicate logic), State (computer science), Lyapunov function

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