Local input-to-state stabilization and ℓ ∞ -induced norm control of discrete-time quadratic systems.

This paper addresses the problems of local stabilization and control of open-loop unstable discrete-time quadratic systems subject to persistent magnitude bounded disturbances and actuator saturation. Firstly, for some polytopic region of the state-space containing the origin, a method is derived to design a static nonlinear state feedback control law that achieves local input-to-state stabilization with a guaranteed stability region under nonzero initial conditions and persistent bounded disturbances. Secondly, the stabilization method is extended to deliver an optimized upper bound on the ℓ _∞ -induced norm of the closed-loop system for a given set of persistent bounded disturbances. Thirdly, the stabilization and ℓ _∞ designs are adapted to cope with actuator saturation by means of a generalized sector bound constraint. The proposed controller designs are tailored via a finite set of state-dependent linear matrix inequalities. Numerical examples are presented to illustrate the potentials of the proposed control design methods. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]