On the Computation of the Induced L_2 Norm of Single
Input Linear Systems with Saturation
B.G. Romanchuk
To appear in the IEEE Transactions on Automatic Control, and available as
Technical Report CUED/F-INFENG/TR. 184. A version was presented at the 33rd
CDC.
In this paper, a means of determining an upper bound of the induced
L_2 norm for a class of single input linear systems with saturation
is given in terms of the existence of a candidate function which satisfies
three differential inequalities. This amounts to a generalisation of
finding the solution of a single algebraic Riccati equation in the linear
problem. A technique to calculate such a function for systems with linear
controllers is also developed. A worked first order example is then
presented. The operator norm is tightly bounded by the use of a piecewise
smooth candidate function which is quadratic within a certain region and
cubic outside.