control with unstable and nonproper weights for descriptor systems

This paper is concerned with a nonstandard H ∞ output feedback control problem for continuous-time descriptor systems, where unstable and nonproper weighting functions are used. Based on two generalized Sylvester equations and two generalized algebraic Riccati equations (GAREs) together with a spectral radius condition, an explicit parametrization of all desirable controllers is deduced. A numerical example is included to illustrate the validity of the proposed result.