New conditions for the finite-time stability of stochastic linear time-varying systems

Abstract

In this paper we investigate the stochastic finitetime stability (SFTS) problem for linear time-varying systems.The system under consideration is described by an Itô type differential equation and the Itô differentiation rule is exploited to derive conditions for SFTS. The main contribution of the paper is that we use an approach based on timevarying quadratic Lyapunov functions, which allow us to obtain less conservative conditions than the time-invariant Lyapunov functions commonly used in the literature. More specifically, we obtain a sufficient condition based on the solution of a generalized Lyapunov differential equation (GLDE) and a sufficient condition requiring the solution of a feasibility problem involving a differential LMIs (DLMI) constraint. We shall show that the DLMI based condition is less conservative and is useful to develop a sufficient condition for stochastic finite-time stabilizability via state feedback; on the other hand the GLDE condition is more efficient from the computational point of view.

Conditions for annular finite‐time stability of Itô stochastic linear time‐varing systems with Markov switching

“…From (14) and (15), the proof follows. □ Note that we need to fix the value of ϵ in (11), in order to obtain a DLMIs-based feasibility problem.…”

“…In [13,15], the concept of FTS has been extended to the class of SLTV Itô systems, while in the recent paper [16], stochastic FTS has been discussed for the class of Markov jump linear timevarying systems. Finally, in [17], the annular stochastic finite-time stability (ASFTS) and stabilisation problems have been tackled for the class of Itô systems with Markov switching.…”

Security control for Markovian jump systems under fading channel: A finite‐time sliding‐mode method

“…Definition 1 (Stochastic finite-time boundedness, SFTB 37 ). For a specified short time T, scalars 0 < 𝛾 1 < 𝛾 2 , and matrix G > 0, if the following inequality holds…”

On finite time stability with guaranteed cost control of uncertain linear systems

“…Among others, some fundamental results on FTS of linear system have been extensively discussed in [1,3,9], the robustness problem has been considered in [4] for uncertain linear systems, whereas stochastic systems are studied in [6,31,32]. FTS for nonlinear systems have been comprehensively addressed in [18].…”