Stability analysis of non-linear systems with multi-input signals sampled and logarithmic quantised in the framework of hybrid systems

This study is to estimate the bounds for the maximum allowable sampling interval (MASI) and the coarsest quantisation density (CQD) that guarantee the stability of non-linear systems with multi-input signals sampled and logarithmic quantised. First of all, hybrid feedback systems are proposed to describe the non-linear control systems. Then a sufficient condition is provided to ensure that the systems are uniformly globally exponentially stable. A crucial step is to find a novel Lyapunov function to verify the stability conditions in the sense of the hybrid framework. Meanwhile, explicit bounds for the MASI and CQD are obtained to guarantee stability. Furthermore, in the case of no quantisation or no sampling, some special stability criteria can be also obtained. Finally, some examples are given to illustrate the effectiveness of the proposed theorem.