Controller design for linear multivariable feedback systems with stable plants, using optimization with inequality constraints†

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Abstract
This paper proposes a two-part design method for unity-feed back linear multivariable systems with stable plants. First, a known algebraic technique yields a matrix Q, with the property that the family of exponentially stable and proper Q globally parametrizes the family of exponentially stable closed-loop systems with proper controllers. Second, having obtained such a family of Qs, a non-linear programming problem is formulated, which when solved, will yield the best feasible Q, with respect to designer-specified objective and constraint functions. The method developed makes possible the systematic formulation and solution of a class of design problems which represent practical design considerations as inequality constraints in non-linear programming problems. Several new design problem formulations are given, and then solved, for some specific plants. These formulations include, for example, constraints to avoid plant saturation, and the mixing of time and frequency domain objectives and constraints.