On finite-gain stabilizability of linear systems subject to input saturation. (English) Zbl 0855.93077

Liu, Wensheng; Chitour, Yacine; Sontag, Eduardo

SIAM J. Control Optimization 34, No. 4, 1190-1219 (1996).

The paper deals with (global) finite-gain input/output stabilization of linear systems with saturated controls, i.e. \(\dot x = Ax + B\sigma(Fx + u)\), where \(x\in \mathbb{R}^n\), \(u\in \mathbb{R}^m\), \(\sigma\) a saturation function and \(A\), \(B\) and \(F\) matrices of appropriate size. For systems with \(A\) neutral, that is, all eigenvalues either in the open left half plane or with some simple eigenvalues at the origin, it is shown that there exists a feedback matrix \(F\) which makes the system \(L^p\)-stable for all \(1\leq p\leq \infty\). Extensions of the problem, including certain perturbation terms, or based upon an output feedback (observer) design, are also given. By means of a counterexample, it is shown that the results are untrue for matrices \(A\) having non-simple eigenvalues at the imaginary axis.

Reviewer: H.Nijmeijer (Enschede)

MSC:

93D25	Input-output approaches in control theory
93D15	Stabilization of systems by feedback

Keywords:

input-saturation; finite-gain stability; input/output stabilization; linear systems; saturated controls; \(L^ p\)-stable