Observer Design for Nonlinear Singular Systems
Observer design for singular systems has been an active field of research in the past several decades. In this chapter, observer design for a class of nonlinear singular systems is studied. The involved nonlinear term satisfies a given quadratic inequality. Under this condition, the error system is expressed by a Lur’e singular system. As a result, the convergency of the estimate error is reduced to the stability of the Lur’e singular system. By virtue of the basic idea of absolute stability, a unified design method for full-order and reduced-order observer is derived. A class of nonlinear singular systems with disturbances is considered. Both of the state equation and the output equation of the systems contain slope-restricted nonlinear terms. An H ∞ observer is designed such that the error system is exponentially stable and the decay rate is bigger than or equal to a given constant and the H ∞ performance of the error system is less than or equal to a prescribed level. Furthermore, two convex optimization algorithms are given to optimize the decay rate and the H ∞ performance, respectively.
KeywordsSingular System Observer Design Quadratic Inequality Linear Singular System Nonlinear Singular System
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