Journal ArticleDOI
Stability margins of singular perturbation systems via state-feedback control
TLDR
In this article, the stability margins of singular perturbation systems are analyzed under unmodelled high-frequency dynamics control, composite control, and the original full-order linear quadratic (LQ) control.Abstract:
The gain and phase margins of singular perturbation systems are analysed under unmodelled high-frequency dynamics control, composite control, and the original full-order linear quadratic (LQ) control. The analysis is on the basis that there is a good relation between the minimum singular value of return difference transfer matrix and the stability margins. We begin with the examination of stability margins of subsystems and then show that state-feedback control design of subsystems could preserve gain and phase margins for the original full-order singularly perturbed system if the singular perturbation parameter epsiv; is sufficiently small.
The effectiveness of e on stability margins is formulated and determined. It is found that the effectiveness can be evaluated by a simple method. Two examples are exploited to illustrate the analytic results.read more
Citations
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Journal ArticleDOI
An infinite /spl epsiv/-bound stabilization design for a class of singularly perturbed systems
TL;DR: In this paper, the state feedback gain matrices can be determined to guarantee the stability of the singularly perturbed systems for all /spl epsiv/spl isin/(0,/spl infin/).
Journal ArticleDOI
Robust control for a class of uncertain state‐delayed singularly perturbed systems
TL;DR: In this paper, the authors considered the problem of robust control for a class of uncertain state-delayed singularly perturbed systems with norm-bounded nonlinear uncertainties and showed that the state feedback gain matrices can guarantee the stability of the closed-loop system for all ), 0 ( ∞ ∈ e and independently of the time delay.
Journal ArticleDOI
Robust stability and stabilization for descriptor systems with uncertainties in all matrices
Shengnan Cheng,Qingling Zhang +1 more
TL;DR: In this paper, the robust stability and stabilization via state feedback for a class of continuous linear time-invariant descriptor systems with norm-bounded perturbations in derivative matrix E and other systems matrices A and B were studied.
Journal ArticleDOI
Robust control for a class of uncertain state-delayed singularly perturbed systems
TL;DR: It is shown that the state feedback gain matrices can be determined to guarantee the stability of the closed-loop system for all e ∈ (0, ∞) and independently of the time delay.
Proceedings Article
Further results on control of singularly perturbed time-delayed systems with nonlinear uncertainties
Makki Bahador,Makki Baharak +1 more
TL;DR: In this paper, a robust control design for singularly perturbed systems with time delays and norm-bounded nonlinear uncertainties is proposed. But the model under investigation considers discrete delays in both slow and fast dynamics and some sufficient conditions are developed in terms of linear matrix inequalities (LMIs).
References
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Journal ArticleDOI
Robustness results in linear-quadratic Gaussian based multivariable control designs
TL;DR: In this paper, the robustness of control systems with respect to model uncertainty is considered using simple frequency domain criteria and new results are derived under a common framework in which the minimum singular value of the return differences transfer matrix is the key quantity.
Journal ArticleDOI
Gain and phase margin for multiloop LQG regulators
TL;DR: Multi-loop linear-quadratic state-feedback regulators are shown to be robust against a variety of large dynamical, time-varying, and non-linear variations in open-loop dynamics, strengthening the link between classical and modern feed-back theory.
Journal ArticleDOI
Principal gains and principal phases in the analysis of linear multivariable feedback systems
TL;DR: In this article, the concept of principal gain and principal phase were introduced for linear multivariable systems, and their use in the analysis of feedback behavior was demonstrated, and a sufficient Nyquist-type stability criterion was presented in terms of these quantities and used to characterize the robustness of the closed-loop stability property when the system model is subjected to a linear perturbation (either multiplicative or additive) at any point in the feedback configuration.
Journal ArticleDOI
Synthesis of state feedback control laws with a specified gain and phase margin
Per Molander,Jan C. Willems +1 more
TL;DR: In this article, it is shown how one may use a "circle criterion" philosophy to design a state feedback control law which yields a closed-loop system with specified robustness characteristics.
Journal ArticleDOI
Multivariable stability-margin optimisation with decoupling and output regulation
M.G. Safonov,B.S. Chen +1 more
TL;DR: In this paper, a procedure is developed for maximising frequency-weighted stability-margin singular values for a multivariable linear time-invariant feedback control system subject to design constraints requiring decoupling and asymptotic tracking in the presence of unstable command and disturbance signals and closed-loop stability.
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