The fixed order decentralized performance problem is formulated as a quadratically constrained control problem in terms of a stable map and the degrees of freedom of the controller. This problem is of the same type as the decentralized and/or simultaneous performance problems that have been discussed in our earlier work, thus the same truncation-based solution procedure can be employed. The proposed approach is demonstrated through an example where the optimal parameter setting for decentralized P and PI control are identified.
The goal of this paper is the calculation of the nonlinearity measure of a nonlinear system over a bounded set of input signals. A relaxation procedure is proposed that employs converging upper and lower bounds to the value of the nonlinearity measure. For a nonlinear BIB0 stable system, the calculation of the lower bound reduces to a sequence of linear programming problems. If in addition, the system is realized as a second order Volterra operator, the upper bound is calculated through global solution of an indefinite quadratic program.
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