Robust finite-time H ∞ control of stochastic jump systems

Abstract

This paper provides the stochastic finite-time stabilization and H ∞ control problem of Markov jump systems with norm-bounded uncertainties and state delays that possess randomly jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. The finite-time H ∞ controller via state feedback is provided to guarantee the stochastic finite-time boundedness and stochastic finite-time stabilization of the resulting closed-loop system for all admissible uncertainties and unknown time-delays. The control criterion is formulated in the form of linear matrix inequalities and the designed finite-time stabilization controller is described as an optimization one. Simulation results illustrate the effectiveness of the developed approaches.

Finite-Time H ∞ State Estimation for Markovian Jump Neural Networks with Time-Varying Delays via an Extended Wirtinger’s Integral Inequality

“…Definition 1 (stochastically finite-time stable (SFTS) [27]). Given time constant T > 0, an MJNN defined as (7) with w(t) � 0 is SFTS with respect to (c 1 , c 2 , T, R) if there exists a positive matrix R > 0 and scalars c 1 > 0 and c 2 > 0, such that the following inequality holds:…”

“…We also studied that finite-time stability involves dynamical systems whose part of the trajectory converges to an equilibrium state in a finite time. Note that the finite-time stability with control frameworks has gained significant attention in recent years [25][26][27][28]. In [29], the authors discussed the finitetime L 2 -gain performance of MJNNs.…”

Sufficient Conditions on the Exponential Stability of Neutral Stochastic Differential Equations with Time-Varying Delays

“…Meanwhile, the delay-independent conditions in [6,10] are restricted when the delay is small. On the other hand, some results are proposed on stochastic Markovian jumping systems (e.g., [13][14][15][16][17][18][19][20]) and finite-time problems of stochastic systems (e.g., [18][19][20][21][22]), which can provide some useful methods and techniques for the neutral stochastic systems. This paper aims to develop the exponential stability in almost sure sense of the neutral stochastic differential equations with time-varying delays.…”

Robust Finite-TimeH∞Control for Nonlinear Markovian Jump Systems with Time Delay under Partially Known Transition Probabilities

“…Meanwhile, the scholars attach more importance to the 𝐻 ∞ control problem, which is to find a stable controller such that the disturbance attenuation level 𝛾 is below a prescribed level. There are a great number of useful and interesting results about 𝐻 ∞ control problem for linear and nonlinear Markovian jump systems in the literature [20][21][22][23][24][25]. To the best of our knowledge, the synthesis issue of robust finite-time 𝐻 ∞ control for nonlinear Markovian jump systems with time delay under partially known transition probabilities has not been fully investigated until now, which motivates us to carry out the present study.…”