Monotonicity of performance with respect to its specification in H ^∞ control

Abstract

Assume that the plant to be controlled is represented by the transfer function matrix P(s), i.e.,

$$ \left[ {\begin{array}{*{20}{c}} {z\left( s \right)} \\ {y\left( s \right)} \end{array}} \right] = P\left( s \right)\left[ {\begin{array}{*{20}{c}} {w\left( s \right)} \\ {u\left( s \right)} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {{P_{11}}\left( s \right)}&{{P_{12}}\left( s \right)} \\ {{P_{21}}\left( s \right)}&{{P_{22}}\left( s \right)} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {w\left( s \right)} \\ {u\left( s \right)} \end{array}} \right], $$

((27.1))

where z(s) denotes an m-dimensional vector of errors to be controlled, y(s) q-dimensional observation vector, w(s) r-dimensional vector of exogeneous signals and u(s) denotes p-dimensional vector of control input.