A novel interval partitioning approach to finite time stability of LTI systems

Abstract

The paper addresses the finite time stability analysis of continuous-time LTI systems. Based on its definition, the necessary and sufficient condition can be derived easily. Verification of the condition is almost impossible because an infinite numbers of checking points are required. Therefore, by using the well-known Bellman-Gronwall inequality, a set of more efficient and practical LMI-based conditions for solving the problem is obtained. In viewing of relaxing the conservativeness of the LMIs, the concept of partitioning the time interval of finite time stability is exploited and a new set of less conservative LMIs are proposed. Moreover, a theoretical proof to show the reduction of conservativeness is given. Simple examples are used to illustrate the improvement of the proposed approach.