Pole shifting with modal dissipative control

The design of state feedback controllers for linear time-invariant systems is considered. There is no difficulty in such a problem, if the control objective is explicitly specified in terms of a standard pole placement problem or a linear quadratic regulator problem. In a realistic situation, however, the design parameters often need to be adjusted by trial and error. This paper aims at reducing such difficulties by eliminating too much freedom in the design parameters, while retaining sufficient room for adjustment during the design procedure. We propose an iterative design method for constructing a state feedback gain, where a single mode of the system is altered in each step of the iteration. Here, we require that a dissipation inequality with a positive definite quadratic supply rate and storage is to be satisfied at all times. This method corresponds to posing an additional restriction in the selection of the weighting matrix within the standard linear quadratic regulator. This helps in keeping the overall balance in the construction of the feedback gain, avoiding inappropriate choice of weighting matrices or closed-loop poles from robustness point of view. The effectiveness of the proposed method is illustrated by a numerical example.