A Linear Programming Approach for Regional Pole Placement Under Pointwise Constraints

Abstract

This paper considers the problem of control of discrete-time linear systems under several complicating features frequently encountered in practice : uncertain parameters in the model, additive noise, linear symmetrical state and input constraints. The main control design objective, beyond local stabilization, is to locate the closed-loop poles in a ”good” region of the unit disc of the complex plane. The originality of the proposed approach is to use Linear Programming as the basic design tool. It is shown that the conditions derived from positive invariance relations and design constraints can be formulated as linear matrix equalities and vector inequalities. The control design problem can then be solved by Linear Programming, with an objective function describing the search for a trade-off between several design objectives.