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

Pagavathigounder Balasubramaniam, Shanmugam Lakshmanan, Rajan Rakkiyappan (2012)

International Journal of Applied Mathematics and Computer Science

This 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...

LMI-based adaptive fuzzy integral sliding mode control of mismatched uncertain systems

Chaouki Mnasri, Moncef Gasmi (2011)

International Journal of Applied Mathematics and Computer Science

Integral sliding mode design is considered for a class of uncertain systems in the presence of mismatched uncertainties in both state and input matrices, as well as norm-bounded nonlinearities and external disturbances. A sufficient condition for the robust stability of the sliding manifold is derived by means of linear matrix inequalities. The initial existence of the sliding mode is guaranteed by the proposed control law. The improvement of the proposed control scheme performances, such as chattering...

Model-free reconfiguration mechanism for fault tolerance

Tushar Jain, Joseph J. Yamé, Dominique Sauter (2012)

International Journal of Applied Mathematics and Computer Science

The problem of fault tolerant control is studied from the behavioral point of view. In this mathematical framework, the concept of interconnection among the variables describing the system is a key point. The problem is that the behavior we intend to control is not known. Therefore, we are interested in designing a fault accommodation scheme for an unknown behavior through an appropriate behavioral interconnection. Here we deal simply with the trajectories that are generated by the system in real...

Monitoring of chlorine concentration in drinking water distribution systems using an interval estimator

Rafał Łangowski, Mietek Brdys (2007)

International Journal of Applied Mathematics and Computer Science

This paper describes the design of an interval observer for the estimation of unmeasured quality state variables in drinking water distribution systems. The estimator utilizes a set bounded model of uncertainty to produce robust interval bounds on the estimated state variables of the water quality. The bounds are generated by solving two differential equations. Hence the numerical efficiency is sufficient for on-line monitoring of the water quality. The observer is applied to an exemplary water...

Observer design for systems with unknown inputs

Stefen Hui, Stanisław Żak (2005)

International Journal of Applied Mathematics and Computer Science

Design procedures are proposed for two different classes of observers for systems with unknown inputs. In the first approach, the state of the observed system is decomposed into known and unknown components. The unknown component is a projection, not necessarily orthogonal, of the whole state along the subspace in which the available state component resides. Then, a dynamical system to estimate the unknown component is constructed. Combining the output of the dynamical system, which estimates the...

On solutions set of a multivalued stochastic differential equation

Marek T. Malinowski, Ravi P. Agarwal (2017)

Czechoslovak Mathematical Journal

We analyse multivalued stochastic differential equations driven by semimartingales. Such equations are understood as the corresponding multivalued stochastic integral equations. Under suitable conditions, it is shown that the considered multivalued stochastic differential equation admits at least one solution. Then we prove that the set of all solutions is closed and bounded.

Optimal estimator of hypothesis probability for data mining problems with small samples

Andrzej Piegat, Marek Landowski (2012)

International Journal of Applied Mathematics and Computer Science

The paper presents a new (to the best of the authors' knowledge) estimator of probability called the "Epₕ√2 completeness estimator" along with a theoretical derivation of its optimality. The estimator is especially suitable for a small number of sample items, which is the feature of many real problems characterized by data insufficiency. The control parameter of the estimator is not assumed in an a priori, subjective way, but was determined on the basis of an optimization criterion (the least absolute...

Pole placement and mixed sensitivity of LTI MIMO systems having controlled outputs different from measurements

Miguel A. Flores, René Galindo (2021)

Kybernetika

Multi-Input Multi-Output (MIMO) Linear Time-Invariant (LTI) controllable and observable systems where the controller has access to some plant outputs but not others are considered. Analytical expressions of coprime factorizations of a given plant, a solution of the Diophantine equation and the two free parameters of a two-degrees of freedom (2DOF) controller based on observer stabilizing control are presented solving a pole placement problem, a mixed sensitivity criterion, and a reference tracking...

RGB-D terrain perception and dense mapping for legged robots

Dominik Belter, Przemysław Łabecki, Péter Fankhauser, Roland Siegwart (2016)

International Journal of Applied Mathematics and Computer Science

This paper addresses the issues of unstructured terrain modeling for the purpose of navigation with legged robots. We present an improved elevation grid concept adopted to the specific requirements of a small legged robot with limited perceptual capabilities. We propose an extension of the elevation grid update mechanism by incorporating a formal treatment of the spatial uncertainty. Moreover, this paper presents uncertainty models for a structured light RGB-D sensor and a stereo vision camera used...

Robust and reliable H output feedback control for linear systems with parameter uncertainty and actuator failure

Chang-Jun Seo, Byung Kook Kim (1999)

Kybernetika

The robust and reliable H output feedback controller design problem is investigated for uncertain linear systems with actuator failures within a prespecified subset of actuators. The uncertainty considered here is time- varying norm-bounded parameter uncertainty in the state matrix. The output of a faulty actuator is assumed to be any arbitrary energy-bounded signal. An observer-based output feedback controller design is presented which stabilizes the plant and guarantees an H -norm bound on attenuation...

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