$H_\infty $ sliding mode control for Markov jump systems with interval time-varying delays and general transition probabilities

Lingchun Li; Guangming Zhang; Meiying Ou; Yujie Wang

Displaying similar documents to “ $H_{\infty}$ sliding mode control for Markov jump systems with interval time-varying delays and general transition probabilities”

Robust observer-based finite-time $H_{\infty}$ control designs for discrete nonlinear systems with time-varying delay

Yali Dong, Huimin Wang, Mengxiao Deng (2021)

Kybernetika

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This paper investigates the problem of observer-based finite-time $H_{\infty}$ control for the uncertain discrete-time systems with nonlinear perturbations and time-varying delay. The Luenberger observer is designed to measure the system state. The observer-based controller is constructed. By constructing an appropriated Lyapunov-.Krasovskii functional, sufficient conditions are derived to ensure the resulting closed-loop system is $H_{\infty}$ finite-time bounded via observer-based control. The observer-based...

Tangential Markov inequality in $L^{p}$ norms

Agnieszka Kowalska (2015)

Banach Center Publications

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In 1889 A. Markov proved that for every polynomial p in one variable the inequality $| | p^{'} {| |}_{[- 1, 1]} {\leq (d e g p) ² | | p | |}_{[- 1, 1]}$ is true. Moreover, the exponent 2 in this inequality is the best possible one. A tangential Markov inequality is a generalization of the Markov inequality to tangential derivatives of certain sets in higher-dimensional Euclidean spaces. We give some motivational examples of sets that admit the tangential Markov inequality with the sharp exponent. The main theorems show that the results on certain arcs...

Output feedback $H_{\infty}$ control of networked control systems based on two channel event-triggered mechanisms

Yanjun Shen, Zhenguo Li, Gang Yu (2021)

Kybernetika

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In this paper, we study dynamical output feedback $H_{\infty}$ control for networked control systems (NCSs) based on two channel event-triggered mechanisms, which are proposed on both sides of the sensor and the controller. The output feedback $H_{\infty}$ controller is constructed by taking random network-induced delays into consideration without data buffer units. The controlled plant and the output feedback controller are updated immediately by the sampled input and the sampled output, respectively. By...

Eigenvalues of operators in $L_{p}$ -spaces in Markov chains with a general state space

Zbyněk Šidák (1967)

Czechoslovak Mathematical Journal

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Compact subsets of $C^{n}$ preserving Markov’s inequality

W. Plesniak (1988)

Matematički Vesnik

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A tracking controller design with preview action for a class of nonlinear Lur'e systems with time-varying delays and external disturbances

Xiao Yu, Fucheng Liao (2021)

Kybernetika

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In this paper, the tracking control problem for a class of discrete-time nonlinear Lur’e systems with time-varying delays and external disturbances is studied via a preview control method. First, a novel translation approach is introduced to construct the augmented error system for Lur’e systems. The output tracking problem is thereby transformed into a guaranteed cost $H_{\infty}$ controller design problem. To produce an integral control action that can eliminate the static error, a discrete integrator...

The scaling limits of a heavy tailed Markov renewal process

Julien Sohier (2013)

Annales de l'I.H.P. Probabilités et statistiques

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In this paper we consider heavy tailed Markov renewal processes and we prove that, suitably renormalised, they converge in law towards the $α$ -stable regenerative set. We then apply these results to the strip wetting model which is a random walk $S$ constrained above a wall and rewarded or penalized when it hits the strip $[0, \infty) \times [0, a]$ where $a$ is a given positive number. The convergence result that we establish allows to characterize the scaling limit of this process at criticality.

Distortion inequality for the Frobenius-Perron operator and some of its consequences in ergodic theory of Markov maps in $ℝ^{d}$

Piotr Bugiel (1998)

Annales Polonici Mathematici

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Asymptotic properties of the sequences (a) ${P_{φ}^{j} g}_{j = 1}^{\infty}$ and (b) ${j^{- 1} \sum_{i = 0}^{j - 1} P ⁱ_{φ} g}_{j = 1}^{\infty}$ , where $P_{φ} : L ¹ \to L ¹$ is the Frobenius-Perron operator associated with a nonsingular Markov map defined on a σ-finite measure space, are studied for g ∈ G = f ∈ L¹: f ≥ 0 and ⃦f ⃦ = 1. An operator-theoretic analogue of Rényi’s Condition is introduced. It is proved that under some additional assumptions this condition implies the L¹-convergence of the sequences (a) and (b) to a unique g₀ ∈ G. The general result is applied to some smooth Markov...

The Nagaev-Guivarc’h method via the Keller-Liverani theorem

Loïc Hervé, Françoise Pène (2010)

Bulletin de la Société Mathématique de France

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The Nagaev-Guivarc’h method, via the perturbation operator theorem of Keller and Liverani, has been exploited in recent papers to establish limit theorems for unbounded functionals of strongly ergodic Markov chains. The main difficulty of this approach is to prove Taylor expansions for the dominating eigenvalue of the Fourier kernels. The paper outlines this method and extends it by stating a multidimensional local limit theorem, a one-dimensional Berry-Esseen theorem, a first-order...

An optimal strong equilibrium solution for cooperative multi-leader-follower Stackelberg Markov chains games

Kristal K. Trejo, Julio B. Clempner, Alexander S. Poznyak (2016)

Kybernetika

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This paper presents a novel approach for computing the strong Stackelberg/Nash equilibrium for Markov chains games. For solving the cooperative $n$ -leaders and $m$ -followers Markov game we consider the minimization of the $L_{p} -$ norm that reduces the distance to the utopian point in the Euclidian space. Then, we reduce the optimization problem to find a Pareto optimal solution. We employ a bi-level programming method implemented by the extraproximal optimization approach for computing the strong...

Model following control system with time delays

Dazhong Wang, Shujing Wu, Wei Zhang, Guoqiang Wang, Fei Wu, Shigenori Okubo (2016)

Kybernetika

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Design of model following control system (MFCS) for nonlinear system with time delays and disturbances is discussed. In this paper, the method of MFCS will be extended to nonlinear system with time delays. We set the nonlinear part $f (v (t))$ of the controlled object as $| | f (v (t)) | | \leq α + {β | | v (t) | |}^{γ}$ , and show the bounded of internal states by separating the nonlinear part into $γ \geq 0$ . Some preliminary numerical simulations are provided to demonstrate the effectiveness of the proposed method.

Two stationarity conditions in the $G I / r_{0} / M / r_{1}$ dam

M. Jankiewicz (1988)

Applicationes Mathematicae

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Markov's property for kth derivative

Mirosław Baran, Beata Milówka, Paweł Ozorka (2012)

Annales Polonici Mathematici

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Consider the normed space $(ℙ (ℂ^{N}), | | \cdot | |)$ of all polynomials of N complex variables, where || || a norm is such that the mapping $L_{g} : (ℙ (ℂ^{N}), | | \cdot | |) ∋ f \mapsto g f \in (ℙ (ℂ^{N}), | | \cdot | |)$ is continuous, with g being a fixed polynomial. It is shown that the Markov type inequality $| \partial / \partial z_{j} {P | | \leq M (d e g P)}^{m} | | P | |$ , j = 1,...,N, $P \in ℙ (ℂ^{N})$ , with positive constants M and m is equivalent to the inequality $| | \partial^{N} / \partial z ₁ . . . \partial z_{N} P | | \leq M^{'} {(d e g P)}^{m^{'}} | | P | |$ , $P \in ℙ (ℂ^{N})$ , with some positive constants M’ and m’. A similar equivalence result is obtained for derivatives of a fixed order k ≥ 2, which can be more specifically formulated in the language of normed algebras....

Sets with the Bernstein and generalized Markov properties

Mirosław Baran, Agnieszka Kowalska (2014)

Annales Polonici Mathematici

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It is known that for $C^{\infty}$ determining sets Markov’s property is equivalent to Bernstein’s property. We are interested in finding a generalization of this fact for sets which are not $C^{\infty}$ determining. In this paper we give examples of sets which are not $C^{\infty}$ determining, but have the Bernstein and generalized Markov properties.

Displaying similar documents to “ H ∞ sliding mode control for Markov jump systems with interval time-varying delays and general transition probabilities”

Displaying similar documents to “ $H_{\infty}$ sliding mode control for Markov jump systems with interval time-varying delays and general transition probabilities”