Robust stability of singularly perturbed state feedback systems using unified approach

Kaur, Hardev; Brown, R.H.; Naidu, D. Subbaram

doi:10.1049/ip-cta:20010681

Cited by 26 publications

(9 citation statements)

References 13 publications

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“…For a system with fast controls, the difference between the maximum and minimum eigenvalues can be very large [18] . Thus, the decay speeds of fast and slow manifolds are very different [19,20] . If applied to such singular systems, the above method requires a very large computational burden and it suffers some other numerical problems (such as truncation error, etc.).…”

Section: Introductionmentioning

confidence: 99%

A reduced-order method for estimating the stability region of power systems with saturated controls

et al. 2007

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In a modern power system, there is often large difference in the decay speeds of transients. This could lead to numerical problems such as heavy simulation burden and singularity when the traditional methods are used to estimate the stability region of such a dynamic system with saturation nonlinearities. To overcome these problems, a reduced-order method, based on the singular perturbation theory, is suggested to estimate the stability region of a singular system with saturation nonlinearities. In the reduced-order method, a low-order linear dynamic system with saturation nonlinearities is constructed to estimate the stability region of the primary high-order system so that the singularity is eliminated and the estimation process is simplified. In addition, the analytical foundation of the reduction method is proven and the method is validated using a test power system with 3 buses and 5 machines.saturation nonlinearity, power system stabilizer, linear matrix inequality, singular perturbation method, reduced-order method

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Section: Introductionmentioning

confidence: 99%

A reduced-order method for estimating the stability region of power systems with saturated controls

et al. 2007

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“…Specifically, we design an integral-type switching surface as given in (9) so that the dynamics restricted to the switching surface (i.e., the sliding mode dynamics) has the form of (16). Observe that (18) is not a LMI due to the existence of the nonlinearity term .…”

Section: Remarkmentioning

confidence: 99%

“…This is due to not only theoretical interests but also the relevance of this topic in control engineering applications. During the past years, the robust stability and stabilization problems of singularly perturbed systems have been widely studied, and many significant results and methods have been presented (see [3][4][5][6][7][8][9][10][11][12][13][14][15][16] and the references therein). Reference [3] presented a composite linear controller for robust stability of singularly perturbed linear systems with matching condition uncertainties, in which the maximum stability bound has not been involved.…”

Section: Introductionmentioning

confidence: 99%

Integral Sliding Mode Control of Lur’e Singularly Perturbed Systems

Wang

Liu

2015

Mathematical Problems in Engineering

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This paper investigates the integral sliding mode control problem for Lur' e singularly perturbed systems with sector-constrained nonlinearities. First, we design a proper sliding manifold such that the motion of closed-loop systems with a state feedback controller along the manifold is absolutely stable. To achieve this, we give a matrix inequality-based absolute stability criterion; thus the above problem can be converted into a matrix inequality feasibility problem. In addition, the gain matrix can also be derived by solving the matrix inequality. Then, a discontinuous control law is synthesized to force the system state to reach the sliding manifold and stay there for all subsequent time. Finally, some numerical examples are given to illustrate the effectiveness of the proposed results.

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“…From (10) and Figure 1, the continuous form is obtained as Z t f t 0 @V½xðtÞ; ' x xðtÞ; tÞÞ @xðtÞ mxðtÞ þ @V½xðtÞ; ' x xðtÞ; tÞÞ…”

Section: Unified Form To Continuous Formmentioning

confidence: 99%

“…The work by has aroused interest in delta ðdÞ operators leading to an unified approach to alleviate some of the difficulties associated with the shift operator-based, discrete-time systems. The unified approach has recently been used by one of the authors for singularly perturbed systems [8][9][10] and for optimal control systems with state constraints [11,12]. However, there appears to be no work done so far on a unified result for the basic optimization problem leading to the Euler-Lagrange equation.…”

Section: Introductionmentioning

confidence: 99%

Unified approach for Euler–Lagrange equation arising in calculus of variations

Naidu

Imura

2004

Optim Control Appl Methods

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SUMMARYWe address the development of a unified approach for the necessary conditions for optimization of a functional arising in calculus of variations. In particular, we develop a unified approach for the EulerLagrange equation, that is simultaneously applicable to both shift ðqÞ-operator-based discrete-time systems and the derivative ðd=dtÞ-operator-based continuous-time systems. It is shown that the Euler-Lagrange results that are now obtained separately for continuous-and discrete-time systems can be easily obtained from the unified approach. An illustrative example is given.

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Robust stability of singularly perturbed state feedback systems using unified approach

Cited by 26 publications

References 13 publications

A reduced-order method for estimating the stability region of power systems with saturated controls

A reduced-order method for estimating the stability region of power systems with saturated controls

Integral Sliding Mode Control of Lur’e Singularly Perturbed Systems

Unified approach for Euler–Lagrange equation arising in calculus of variations

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