State-dependent jump linear systems (SJLSs) are a set of linear systems whose switching is determined by a finite state random process with state-dependent transition rates. In this study, a SJLS is considered with state multiplicative noise and stochastic perturbations. In particular, the jump process is regarded to have dissimilar transition rates among sets of state evolution space. The aim of this study is to consider stochastic ℋ∞ control of such systems using state-feedback control input. Sufficient conditions for stochastic ℋ∞ are obtained by solving linear matrix inequalities, which are validated by a simulation example. © The Institution of Engineering and Technology 2018.

Shaikshavali 	 Chitraganti

Department of Electrical Engineering

S. Aberkane

Fulltext

Indian Institute of Technology Palakkad&nbsp;(IIT Palakkad or IIT PKD) is a public autonomous&nbsp;engineering&nbsp;and&nbsp;research&nbsp;institute located in&nbsp;Palakkad,&nbsp;Kerala. It was&nbsp;one of the five new&nbsp;IITs&nbsp;proposed in the&nbsp;2014 Union budget of India. The campus was inaugurated on 3 August 2015. The institute has 94 faculty, 978 students, and 63 non-teaching staffs.

IT Palakkad currently offers four-year Bachelor of Technology (B.Tech) and two years MS programmes in 8 different engineering disciplines including&nbsp;Computer Science, Electrical, Mechanical, Civil among others.

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IIT Palakkad

IET Control Theory and Applications

In this article, we consider a continuous-time state-dependent jump linear system (SDJLS), a kind of stochastic hybrid system, with the presence of uncertainties in system parameters. In SDJLS, we consider that the transition rates of the underlying random jump process depend on the state variable. In particular, we assume the transition rates to have different values across suitably defined sets to which the state of the system belongs, and address a problem of robust stability and stabilization analysis. We obtain sufficient conditions for robust stability and state-feedback stabilization in terms of linear matrix inequalities (LMIs). We validate the obtained sufficient robust stability and stabilization conditions with numerical examples. © 2015 Elsevier Ltd.

Nonlinear Analysis: Hybrid Systems

Robust stabilization of a class of state-dependent jump linear systems

In this article, we consider a receding horizon control of discrete-time state-dependent jump linear systems, a particular kind of stochastic switching systems, subject to possibly unbounded random disturbances and probabilistic state constraints. Due to the nature of the dynamical system and the constraints, we consider a one-step receding horizon. Using inverse cumulative distribution function, we convert the probabilistic state constraints to deterministic constraints, and obtain a tractable deterministic receding horizon control problem. We consider the receding horizon control law to have a linear state-feedback and an admissible offset term. We ensure mean square boundedness of the state variable via solving linear matrix inequalities off-line, and solve the receding horizon control problem on-line with control offset terms. We illustrate the overall approach applied on a macroeconomic system. © 2014 Elsevier B.V. All rights reserved.

Systems and Control Letters

On control of discrete-time state-dependent jump linear systems with probabilistic constraints: A receding horizon approach

Advances in Applied Probability

Optimal replacement under a general failure model

IFAC Proceedings Volumes

Output Feedback H2/H‚àû Control of a Class of Discrete-time Reconfigurable Control Systems

Technometrics

A State-Dependent Wear Model With an Application to Marine Engine Cylinder Liners

Stochastic ℋ∞ control of state-dependent jump linear systems with state-dependent noise

Journal	IET Control Theory and Applications
Publisher	Institution of Engineering and Technology
ISSN	17518644