Exact robust H2 performance analysis for linear single-parameter dependent systems

Exact robust H₂ performance analysis is considered for linear time-invariant continuous-time systems whose coefficient matrices are polynomials of a single parameter. A necessary and sufficient condition for the robust H ₂ performance is derived as a set of parameterized LMIs whose variable matrix is a polynomial of the parameter, where a bound of its degree is given explicitly. Then, the parameterized LMIs are transformed exactly to parameter-independent and finite-dimensional LMIs. The discrete-time counterpart of the above results is also derived.