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IMA Journal of Mathematical Control and Information 1991 8(2):151-164; doi:10.1093/imamci/8.2.151
© 1991 by Institute of Mathematics and its Applications
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Singular-Value Assignment in the Design of Observers for Discrete-Time Systems

D. N. SHIELDS

CTAG Group, Mathematics Dept., Coventry Polytechnic Priory Street, CV1 5FB

This paper examines the optimum choice of a gain matrix H in the design of a full-order observer for a discrete-time descriptor system, which may be singular provided that certain rank conditions are satisfied. The choice forms part of a two-stage design process for designing a robust observer, and the results obtained are applicable to other designs such as those of Dai (1988) and Fahmy et al. (1989). A robust strategy involves the assignment of the singulsr values of a matrix J1 = J – HC where C and J are given, and results are derived for the optimal assignment. The problem of selecting H is then expressed in terms of the minimization of a cost function f(H) over a class H defined such that k2(J1) is a minimum or a constant. An algorithm is proposed for parameterizing H so that the minimization is solvable. A suboptimal, but explicit, solution is given for H which minimizes a bound on ||H||2. The observer design is applied to a simple high-pressure gas network.


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