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**Stability analysis of pulse-width-modulated feedback systems.**
*(English)*
Zbl 0995.93058

Lyapunov’s direct method employing quadratic Lyapunov functions is applied to establish new and improved stability results for pulse-width-modulated (PWM) feedback systems with linear and nonlinear plants. For PWM feedback systems with linear plant, new sufficient conditions for the uniform asymptotic stability in the large of the trivial solution and necessary and sufficient conditions for the uniform ultimate boundedness of the solutions are established. Two cases are considered, first where the linear plant is Hurwitz stable, and then the critical case, where the linear plant has one pole at the origin while the remaining poles, if any, are in the left half of the complex plane. Finally, it is shown that under certain assumptions stability properties of the trivial solution of PWM feedback systems with nonlinear plant can be deduced from the stability properties of the trivial solution of PWM feedback systems with linearized plant, including even the critical case. Comparison with known results is presented with the help of five specific examples reported in the literature.

Reviewer: Svitlana P.Rogovchenko (Famagusta)

### MSC:

93D15 | Stabilization of systems by feedback |

93C57 | Sampled-data control/observation systems |

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |

### Keywords:

pulse-width modulation; linearization; Lyapunov stability; Lagrange stability; Lyapunov function; stabilization; uniform asymptotic stability; critical case
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\textit{L. Hou} and \textit{A. N. Michel}, Automatica 37, No. 9, 1335--1349 (2001; Zbl 0995.93058)

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