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

Mnasri C., Gasmi M.

International Journal of Applied Mathematics and Computer Science

2011

Vol. 21, no 4

605-615

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 elimination and estimation of norm bounds of uncertainties, is then considered with the application of an adaptive fuzzy integral sliding mode control law. The validity and efficiency of the proposed approaches are investigated through a sixth order uncertain mechanical system.

Estimation of the output deviation norm for uncertain, discrete-time nonlinear systems in a state dependent form

Orłowski P.

International Journal of Applied Mathematics and Computer Science

2007

Vol. 17, no 4

505-513

Numerical evaluation of the optimal nonlinear robust control requires estimating the impact of parameter uncertainties on the system output. The main goal of the paper is to propose a method for estimating the norm of an output trajectory deviation from the nominal trajectory for nonlinear uncertain, discrete-time systems. The measure of the deviation allows us to evaluate the robustness of any designed controller. The first part of the paper concerns uncertainty modelling for nonlinear systems given in the state space dependent form. The method for numerical estimation of the maximal norm of the output trajectory deviation with applications to robust control synthesis is proposed based on the introduced three-term additive uncertainty model. Theoretical deliberations are complemented with a numerical, water-tank system example.

Robust performance of a class of control systems

Wang L.

Control and Cybernetics

2004

Vol. 33, no 1

71-83

Some Kharitonov-like robust Hurwitz stability criteria are established for a class of complex polynomial families with nonlinearly correlated perturbations. These results are extended to the polynomial matrix case and non-interval D-stability case. Applications of these results in testing of robust strict positive realness of real and complex interval transfer function families are also presented.

Solution tubes to differential inclusions within a collection of sets

Quincampoix M., Veliov V.

Control and Cybernetics

2002

Vol. 31, no 3

847-862

This paper develops the theory of solution tubes to differential inclusions (uncertain systems) within a prescribed collection of sets. The notion is defined as a minimal invariant tube with values in the collection. Under certain requirements for the collection we prove existence and Lipschitz-like stability of the solution tubes. The theory is relevant to problems of systems estimation in the context of control or differential games.