Design of static linear multivariable output feedback controllers using random optimization techniques

New necessary and sufficient conditions for multivariable pole placement (MVPP) and entire eigenstructure assignment (EEA) through static linear multivariable output feedback are established. It is shown that the resultant matrix is of full rank and all design freedoms are retained. The problem of static linear multivariable output feedback control law design is then defined. Based on the EEA concept and sufficiency of the regional pole placement, the design is (re)formulated in terms of a constrained nonlinear optimization problem. To this end, some decoupling indices for noninteractive performance are defined, their necessary and sufficient conditions are derived and tracker design is addressed. The problem formulation well suits the application of random/intelligent optimization techniques. By way of this approach, optimal robust stability/performance, noninteractive performance, reliability, actuator limitations and low sensitivity in the face of structured or unstructured plant uncertainties are achieved. The effectiveness of the proposed methodology is demonstrated by simulation results using genetic algorithm.

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