Stability Criteria For Stochastic Systems Research Articles

Fixed/Prescribed stability criterions of stochastic system with time-delay

<abstract><p>In this paper, the fixed/prescribed-time stability issues were considered for stochastic systems with time delay. First, some new fixed-time stability and prescribed-time stability criteria for stochastic systems with delay and multi-delay were established. Second, based on the new fixed/prescribed stability criteria, the fixed-time stabilization of the stochastic system with time-delay and the prescribed-time stabilization of the stochastic reaction-diffusion system with multi-delay were investigated, respectively. Third, two new fixed/prescribed-time delay-independent control mechanisms were designed. The primary advantage of the innovative fixed/prescribed-time controller lies in its independence from delayed states. This makes the controller applicable to systems with unknown delays. Finally, three numerical examples were provided to illustrate the feasibility of the stated theoretical results.</p></abstract>

Formula omitted] tracking of uncertain stochastic time-delay systems: Memory state-feedback controller design

The problem of state robust H∞ tracking control for uncertain stochastic systems with interval time-varying delay is considered in this paper. The target is to design a memory state feedback controller such that the resulting closed-loop augmented system is robustly stochastically asymptotically stable and the states of original systems can follow the reference signal with given H∞ performance. Firstly, by constructing delay-partitioning-dependent Lyapunov–Krasovskii functional with reciprocally convex approach, a delay-dependent condition guaranteeing the robust H∞ tracking performance is proposed in a set of matrix inequalities. Secondly, new stability criteria for stochastic systems with time-varying delay are given with less conservativeness than some recent results. Thirdly, memory state feedback controller is designed via a set of linear matrix inequalities (LMIs) which can be solved by Matlab LMI toolbox. At last, numerical simulations are addressed to show the effectiveness of the proposed methods.

LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties

LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertaintiesThis paper studies an LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties. The delay is assumed to be time-varying and belong to a given interval, which means that lower and upper bounds of this interval time-varying delay are available. The uncertainty under consideration includes polytopic-type uncertainty and linear fractional norm-bounded uncertainty. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, delay-dependent stability criteria are obtained in terms of Linear Matrix Inequalities (LMIs). Moreover, the derivative of time delays is allowed to take any value. Finally, four numerical examples are given to illustrate the effectiveness of the proposed method and to show an improvement over some results found in the literature.

Novel delay-dependent stability criteria for stochastic systems with time-varying interval delay

In this paper, the problem of the stability for a class of stochastic systems with time-varying interval delay is investigated. Through constructing a novel Lyapunov-Krasovskii functional and utilizing the information of both the lower and upper bounds of the delay, the delay-dependent sufficient criteria are derived in terms of linear matrix inequalities (LMIs). Neither model transformations nor bounding techniques for cross terms is employed, so the derived criteria are less conservative than the existing results. Meanwhile, the computational complexity of the obtained stability conditions is reduced because fewer variables are involved. Numerical examples are given to show the effectiveness and the benefits of the proposed method.

Delay-dependent exponential stability criteria for stochastic systems with polytopic-type uncertainties

This paper considers the problem of delay-dependent exponential stability in mean square for stochastic systems with polytopic-type uncertainties and time-varying delay. Applying the descriptor model transformation and introducing free weighting matrices, a new type of Lyapunov-Krasovskii functional is constructed based on linear matrix inequalities (LMIs), and some new delay-dependent criteria are obtained. These criteria include the delay-independent/ratedependent and delay-dependent/rate-independent exponential stability criteria. These new criteria are less conservative than existing ones. Numerical examples demonstrate that these new criteria are effective and are an improvement over existing ones.

New delay-dependent stability criterion for stochastic systems with time delays

The problem of concern here is the stability analysis for stochastic systems with a time delay in the state. By employing a novel Lyapunov–Krasovskii functional, a new delay-dependent exponential stability condition is established for such stochastic time-delay systems. Based on the delay fractioning approach, the developed method can greatly reduce conservativeness compared with the existing results. Numerical examples are provided to show the advantage of the proposed techniques.

Stability criteria for stochastic systems with colored multiplicative noise

In this paper a particular class of stochastic systems is considered, described by linear differential equations with multiplicative colored noise parameters; it is assumed that a certain commutativity condition is true. For these systems explicit criteria are derived for the asymptotic stability of the moments of any order and also for almost sure asymptotic stability.

Frequency domain stability criteria for stochastic systems

The stability of a class of dynamical systems containing random parameters is investigated. An input-output stability concept is formulated for stochastic systems. The specific class of systems considered consists of those feedback systems whose open loop consists of the cascade of a white noise multiplicative gain and a linear deterministic dynamical system. Necessary and sufficient frequency domain conditions for stability are derived and it is shown that the uncertainty has a destabilizing effect. The resulting stability conditions depend on the open-loop stability, the rms value of the stochastic gain element, and the effective bandwidth of the linear element.