Exact robust H2 performance analysis for linear parameter dependent systems

Exact robust H₂ performance analysis is investigated for linear time-invariant continuous-time systems whose coefficient matrices are polynomials of uncertain parameters. A necessary and sufficient condition for the robust H₂ performance is derived as a set of parameterized LMIs whose variable matrix is a polynomial of the parameters, where a bound of its degree is given explicitly. The set of the parameterized LMIs is reduced to a set of parameter-independent and finite-dimensional LMIs. Although the derived set of the LMIs is a sufficient condition for the robust H₂ performance, it also attains necessity if the coefficient matrices of the system are polynomials of one uncertain parameter.