Upper and lower bounds of H∞-optimal performance for a class of continuous-time descriptor systems

In this paper, finite- and infinite-horizon H_∞ optimal control problems for a class of linear time-invariant descriptor systems are studied. Using a dynamic game theoretic approach, we provide upper and lower bounds of H_∞-optimal performance, which are characterized in terms of a parameterized reduced-order Riccati-like algebraic equation and a parameterized reduced-order game Riccati differential or algebraic equation. Moreover, we show that, if a prespecified performance level is achievable, the central H_∞ -controller to guarantee such a performance level is not unique. A numerical example is included to illustrate the results obtained in the paper