scholarly journals Consensus and Eigenvalue Estimation in Dynamic Consensus Networks with Strictly Positive Real Systems

2019 ◽  
Vol 1 (3) ◽  
Keyword(s):  
Positive Real ◽  
Strictly Positive Real ◽  
Eigenvalue Estimation

Active Helmholtz Resonator With Positive Real Impedance

2006 ◽  
Vol 129 (1) ◽  
pp. 94-100 ◽  
Author(s):  
Jing Yuan
Keyword(s):  
Noise Control ◽  
Helmholtz Resonator ◽  
Control Device ◽  
Positive Real ◽  
Noise Field ◽  
Strictly Positive Real ◽  
Control Devices ◽  
Passive Noise ◽  
Active Resonator ◽  
Electronic Resonance

The impedance of a passive noise control device is strictly positive real, if the device is installed in noise fields with weak mean flows. Passive noise control devices are, therefore, more reliable than active ones. Active control may be applied to a Helmholtz resonator to introduce electronic resonance. It will affect the impedance Zact of the resonator. A controller may be designed such that (a) Zact is small and resistive at some tunable frequencies; and (b) Re{Zact}⩾0 in the entire frequency range of interest. If criterion (a) is satisfied, the active resonator can suppress duct noise at tunable frequencies. It is difficult to design a controller to satisfy criterion (b) because parameters of the controller depend on acoustic parameters of the noise field. A new method is proposed here to design an active controller to meet both criteria simultaneously. The satisfaction of criterion (b) implies a positive real Zact and a robust active resonator with respect to parameter variation in the noise field. Experimental results are presented to verify the performance of the active resonator.

scholarly journals On the Asymptotic Hyperstability of Linear Time-Invariant Continuous-Time Systems under a Class of Controllers Satisfying Discrete-Time Popov’s Inequality

2018 ◽  
Vol 2018 ◽  
pp. 1-17
Author(s):  
M. De la Sen
Keyword(s):  
Continuous Time ◽  
Linear Time ◽  
Positive Real ◽  
Feedback Controllers ◽  
Linear Time Invariant ◽  
Continuous Time Systems ◽  
Strictly Positive Real ◽  
Forward Transfer ◽  
Time Invariant ◽  
Time Systems

This paper is concerned with the property of asymptotic hyperstability of a continuous-time linear system under a class of continuous-time nonlinear and perhaps time-varying feedback controllers belonging to a certain class with two main characteristics; namely, (a) it satisfies discrete-type Popov’s inequality at sampling instants and (b) the control law within the intersample period is generated based on its value at sampling instants being modulated by two design weighting auxiliary functions. The closed-loop continuous-time system is proved to be asymptotically hyperstable, under some explicit conditions on such weighting functions, provided that the discrete feed-forward transfer function is strictly positive real.

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