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Subject = discrete time systems ;
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Displaying Results 1  5 of 5 on page 1 of 1
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Feedback Stabilization Over SignaltoNoise Ratio Constrained Channels.
(2007)
Braslavsky, Julio H.; Middleton, Richard H.; Freudenberg, James S.
Feedback Stabilization Over SignaltoNoise Ratio Constrained Channels.
(2007)
Braslavsky, Julio H.; Middleton, Richard H.; Freudenberg, James S.
Abstract:
There has recently been significant interest in feedback stabilization problems with communication constraints including constraints on the available data rate. Signaltonoise ratio (SNR) constraints are one way in which datarate limits arise, and are the focus of this paper. In both continuous and discretetime settings, we showthat there are limitations on the ability to stabilize an unstable plant over a SNR constrained channel using finitedimensional linear time invariant (LTI) feedback. In the case of state feedback, or output feedback with a delayfree, minimum phase plant, these limitations in fact match precisely those that might have been inferred by considering the associated ideal Shannon capacity data rate over the same channel. In the case of LTI output feedback, additional limitations are shown to apply if the plant is nonminimum phase. In this case, we show that for a continuoustime nonminimum phase plant, a periodic linear time varying feedback scheme with fast s...
http://mural.maynoothuniversity.ie/1741/
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Input Disturbance Rejection in Channel SignaltoNoise Ratio Constrained Feedback Control
(2008)
Rojas, A.J.; Middleton, R.H.; Freudenberg, J.S.; Braslavsky, J.H.
Input Disturbance Rejection in Channel SignaltoNoise Ratio Constrained Feedback Control
(2008)
Rojas, A.J.; Middleton, R.H.; Freudenberg, J.S.; Braslavsky, J.H.
Abstract:
Communication channels impose a number of obstacles to feedback control. One recent line of work considers the problem of feedback stabilisation subject to a constraint on the channel signaltonoise ratio (SNR). It has been shown for continuoustime systems that the optimal control problem of achieving the infimal SNR can be formulated as a linear quadratic Gaussian (LQG) control problem with weights chosen as in the loop transfer recovery (LTR) technique. The present paper extends this formulation to: discretetime systems; communications over channels with memory; and input disturbance rejection. By using this formulation, we derive exact expressions for the linear time invariant (LTI) controller that achieves the infimal SNR under the effect of timedelay and additive coloured noise. We then quantify the infimal SNR required for both stabilisation and input disturbance rejection for a relative degree one, minimum phase plant and a memoryless Gaussian channel.
http://mural.maynoothuniversity.ie/2245/
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Optimal Signal to Noise Ratio in Feedback over Communication Channels with Memory
(2006)
Rojas, A.J.; Freudenberg, J.S.; Braslavsky, J.H.; Middleton, R.H.
Optimal Signal to Noise Ratio in Feedback over Communication Channels with Memory
(2006)
Rojas, A.J.; Freudenberg, J.S.; Braslavsky, J.H.; Middleton, R.H.
Abstract:
Communication channels impose a number of obstacles to feedback control, such as delay, noise, and constraints in communication datarate. One alternate line of recent work considers the problem of feedback stabilization subject to a constraint in the signaltonoise ratio (SNR). It has been shown for continuoustime systems that the optimal control problem arising in achieving minimal SNR can be formulated as a linear quadratic Gaussian (LQG) control problem with weights chosen as in the loop transfer recovery (LTR) technique. The present paper extends such LQG/LTR formulation to discretetime systems with feedback over channels with memory. By using such formulation, we derive exact expressions for the LTI controller and loop sensitivity functions that achieve minimal SNR under the effect of timedelay, non minimum phase zeros and colored additive noise. For the minimumphase case with white noise and no time delay, we show that the optimal feedback loop obtained after applying LTR...
http://mural.maynoothuniversity.ie/1789/
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Optimal triangular approximation for linear stable multivariable systems.
(2007)
Oyarzún, Diego A.; Salgado, Mario E.
Optimal triangular approximation for linear stable multivariable systems.
(2007)
Oyarzún, Diego A.; Salgado, Mario E.
Abstract:
This paper deals with the problem of obtaining a stable triangular approximation for a linear, square, stable, discretetime MIMO system. We solve this problem through an analytic procedure that yields an explicit solution of a convex optimization problem. The optimized quantity is the L2 norm of the relative modelling error. An interesting feature of the proposed methodology is that, if the MIMO system has nonminimum phase zeros near the stability boundary, then the derived approximation has, at least, a set of zeros close to them. The usefulness of our result comes mainly from its use as nominal model in triangular controller design procedures based on a triangular plant model.
http://mural.maynoothuniversity.ie/1746/
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Preservation of Common Quadratic Lyapunov Functions and Padé Approximations
(2010)
Sajja, Surya; Solmaz, Selim; Shorten, Robert N.; Corless, Martin
Preservation of Common Quadratic Lyapunov Functions and Padé Approximations
(2010)
Sajja, Surya; Solmaz, Selim; Shorten, Robert N.; Corless, Martin
Abstract:
It is well known that the bilinear transform, or first order diagonal Padé approximation to the matrix exponential, preserves quadratic Lyapunov functions between continuoustime and corresponding discretetime linear time invariant (LTI) systems, regardless of the sampling time. It is also well known that this mapping preserves common quadratic Lyapunov functions between continuoustime and discretetime switched systems. In this note we show that while diagonal Padé approximations do not in general preserve other types of Lyapunov functions (or even stability), it is true that diagonal Padé approximations of the matrix exponential, of any order and sampling time, preserve quadratic stability. A consequence of this result is that the quadratic stability of switched systems is robust with respect to certain discretization methods.
http://mural.maynoothuniversity.ie/3826/
Displaying Results 1  5 of 5 on page 1 of 1
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