On the estimate of the domain of validity of non-linear H-infinity control

Certain properties of controllers designed using the non-linear H-infinity technique are studied. It is well known that the explicit solution of the H amilton-Jacobi-Isaacs (HJI) inequality is generally not feasible. In this p aper by applying the polynomial approximation method, approximate expressio ns of the co-state and the two players of the game are considered. Using Ly apunov techniques, we prove a property related to the conjecture by van der Schaft (1993), which states that the non-linear feedback controller always results in a larger domain of validity than its linearized controller. Spe cifically, it is shown that the estimate of the domain of validity grows pr oportionally to the order of the control approximation. Effects of attenuat ion level and weighting the controlled output on the estimate of the domain of validity are also discussed. In this connection, a fictitious autonomou s system derived from the original system and its HJI inequality is first i ntroduced. The effect of approximation is then represented by introducing a perturbation term. It is shown that the estimate of the domain of validity for the HJI inequality may be related to the estimate of the domain of att raction of the equilibrium point of the fictitious system.