Stabilisation of locally Lipschitz non-linear systems under input saturation and quantisation

Abstract

This study addresses the control of locally Lipschitz non-linear systems under quantisation and input saturation non-linearities. The non-linear dynamics of the systems are taken to be locally Lipschitz, rather than the conventional globally Lipschitz counterpart, to consider a generalised form of the Lipschitz non-linear systems. An ellipsoidal region containing the origin is constructed, for which the non-linear dynamics satisfy the Lipschitz condition in contrast to the conventional approaches. Saturation and quantisation non-linearities are dealt using a generalised local sector condition and a bound on the quantisation noise. A regional control strategy for the stabilisation of non-linear systems using state feedback is devised by employing these conditions, which is further extended to attain robustness against external perturbations. The proposed control strategies guarantee convergence of the states of a non-linear system inside a bounded reducible region in the neighbourhood of the origin. In contrast to the conventional approaches, the present study considers ellipsoidally Lipschitz non-linear systems, supports various types of quantisers, ensures attenuation of the disturbances, and provides a clear picture of the region of stability. An example of the application of the proposed control strategies for a modified Chua's circuit is demonstrated.