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Control of linear systems with saturating actuators. (English) Zbl 0853.93046

The paper deals with (linear) systems of the form $\stackrel{˙}{x}=Ax+B\sigma \left(u+g\left(x,t\right)\right)$, $y=Cx$, with $x,u$ and $y$ the state-, input- and output vector; $\sigma$ is a saturation function and $g$ represents the uncertainties/disturbances in the system. The problem addressed is to find a suitable feedback $u=Fx$ (or an output feedback gain) such that i) the closed-loop system is semi-globally stable when $g\equiv 0$, and ii) robust semi-global disturbance rejection is achieved.

Under suitable assumptions on $A,B$ and $C$, the structure of the saturation function $\sigma$ and the structure of the uncertainty function $g$, a solution to the problem is derived. The solution consists of a composite control law which is on the one hand of low gain nature, and, on the other hand of high gain type. The paper unifies some earlier results of the same authors on results dealing with either i) or ii).

##### MSC:
 93B52 Feedback control 93C05 Linear control systems 93D15 Stabilization of systems by feedback