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An H sliding mode observer for Takagi-Sugeno nonlinear systems with simultaneous actuator and sensor faults

Ali Ben Brahim, Slim Dhahri, Fayçal Ben Hmida, Anis Sellami (2015)

International Journal of Applied Mathematics and Computer Science

This paper considers the problem of robust reconstruction of simultaneous actuator and sensor faults for a class of uncertain Takagi-Sugeno nonlinear systems with unmeasurable premise variables. The proposed fault reconstruction and estimation design method with H∞ performance is used to reconstruct both actuator and sensor faults when the latter are transformed into pseudo-actuator faults by introducing a simple filter. The main contribution is to develop a sliding mode observer (SMO) with two...

Controlling a non-homogeneous Timoshenko beam with the aid of the torque

Grigory M. Sklyar, Grzegorz Szkibiel (2013)

International Journal of Applied Mathematics and Computer Science

Considered is the control and stabilizability of a slowly rotating non-homogeneous Timoshenko beam with the aid of a torque. It turns out that the beam is (approximately) controllable with the aid of the torque if and only if it is (approximately) controllable. However, the controllability problem appears to be a side-effect while studying the stabilizability. To build a stabilizing control one needs to go through the methods of correcting the operators with functionals so that they have finally...

Delay differential systems with time-varying delay: new directions for stability theory

James Louisell (2001)


In this paper we give an example of Markus–Yamabe instability in a constant coefficient delay differential equation with time-varying delay. For all values of the range of the delay function, the characteristic function of the associated autonomous delay equation is exponentially stable. Still, the fundamental solution of the time-varying system is unbounded. We also present a modified example having absolutely continuous delay function, easily calculating the average variation of the delay function,...

Design of the state predictive model following control system with time-delay

Dazhong Wang, Shujing Wu, Shigenori Okubo (2009)

International Journal of Applied Mathematics and Computer Science

Time-delay systems exist in many engineering fields such as transportation systems, communication systems, process engineering and, more recently, networked control systems. It usually results in unsatisfactory performance and is frequently a source of instability, so the control of time-delay systems is practically important. In this paper, a design of the state predictive model following control system (PMFCS) with time-delay is discussed. The bounded property of the internal states for the control...

Differential stability of solutions to air quality control problems in urban area

Piotr Holnicki, Jan Sokołowski, Antoni Żochowski (1987)

Aplikace matematiky

The convex optimal control problem for a system described by the parabolic equation is considered. The form of the right derivative of an optimal solution with respect to the parameter is derived. The applications to an air quality control problem are discussed. Numerical result are provided.

Efficiency analysis of control algorithms in spatially distributed systems with chaotic behavior

Łukasz Korus (2014)

International Journal of Applied Mathematics and Computer Science

The paper presents results of examination of control algorithms for the purpose of controlling chaos in spatially distributed systems like the coupled map lattice (CML). The mathematical definition of the CML, stability analysis as well as some basic results of numerical simulation exposing complex, spatiotemporal and chaotic behavior of the CML were already presented in another paper. The main purpose of this article is to compare the efficiency of controlling chaos by simple classical algorithms...

Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains

Piotr Ostalczyk (2012)

International Journal of Applied Mathematics and Computer Science

Two description forms of a linear fractional-order discrete system are considered. The first one is by a fractional-order difference equation, whereas the second by a fractional-order state-space equation. In relation to the two above-mentioned description forms, stability domains are evaluated. Several simulations of stable, marginally stable and unstable unit step responses of fractional-order systems due to different values of system parameters are presented.

Further results on robust fuzzy dynamic systems with LMI 𝓓-stability constraints

Wudhichai Assawinchaichote (2014)

International Journal of Applied Mathematics and Computer Science

This paper examines the problem of designing a robust fuzzy controller with -stability constraints for a class of nonlinear dynamic systems which is described by a Takagi-Sugeno (TS) fuzzy model. Fuzzy modelling is a multi-model approach in which simple sub-models are combined to determine the global behavior of the system. Based on a linear matrix inequality (LMI) approach, we develop a robust fuzzy controller that guarantees (i) the ₂-gain of the mapping from the exogenous input noise to the...

Immunotherapy with interleukin-2: A study based on mathematical modeling

Sandip Banerjee (2008)

International Journal of Applied Mathematics and Computer Science

The role of interleukin-2 (IL-2) in tumor dynamics is illustrated through mathematical modeling, using delay differential equations with a discrete time delay (a modified version of the Kirshner-Panetta model). Theoretical analysis gives an expression for the discrete time delay and the length of the time delay to preserve stability. Numerical analysis shows that interleukin-2 alone can cause the tumor cell population to regress.

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