H-infinity

	H-infinity ''H''∞ (i.e. "''H''-infinity") methods are used in control theory to synthesize controllers to achieve stabilization with guaranteed performance. To use ''H''∞ methods, a control designer expresses the control problem as a mathematical optimization problem and then finds the controller that solves this optimization. ''H''∞ techniques have the advantage over classical control techniques in that ''H''∞ techniques are readily applicable to problems involving multivariate systems with cross-coupling between channels; disadvantages of ''H''∞ techniques include the level of mathematical understanding needed to apply them successfully and the need for a reasonably good model of the system to be controlled. It is important to keep in mind that the resulting controller is only optimal with respect to the prescribed cost function and does not necessarily represent the best controller in terms of the usual performance measures used to evaluate controllers such as settling time, ener ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	H-infinity Loop-shaping H-infinity loop-shaping is a design methodology in modern control theory. It combines the traditional intuition of classical control methods, such as Bode's sensitivity integral, with H infinity, H-infinity optimization techniques to achieve controllers whose stability and performance properties hold despite bounded differences between the nominal plant assumed in design and the true plant encountered in practice. Essentially, the control system designer describes the desired responsiveness and noise-suppression properties by weighting the plant transfer function in the frequency domain; the resulting 'loop-shape' is then 'robustified' through optimization. Robustification usually has little effect at high and low frequencies, but the response around unity-gain crossover is adjusted to maximise the system's stability margins. H-infinity loop-shaping can be applied to multiple-input multiple-output (MIMO) systems. H-infinity loop-shaping can be carried out using commercially avail ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	George Zames George Zames (January 7, 1934 – August 10, 1997) was a Polish-Canadian control theorist and professor at McGill University, Montreal, Quebec, Canada. Zames is known for his fundamental contributions to the theory of robust control, and was credited for the development of various well-known results such as small-gain theorem, passivity theorem, circle criterion in input–output form, and most famously, H-infinity methods. Biography Childhood George Zames was born on January 7, 1934 in Łódź, Poland to a Jewish family. Growing up in Warsaw, Zames and his family escaped the city at the onset of World War II, and moved to Kobe (Japan), through Lithuania and Siberia, and finally to the Anglo-French International Settlement in Shanghai. Zames indicated later that he and his family owe their lives to the transit visa provided by the Japanese Consul to Lithuania, Chiune Sugihara. In Shanghai, Zames continued his schooling, and in 1948, the family emigrated to Canada. Educati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Control Theory Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any ''delay'', ''overshoot'', or ''steady-state error'' and ensuring a level of control stability; often with the aim to achieve a degree of optimality. To do this, a controller with the requisite corrective behavior is required. This controller monitors the controlled process variable (PV), and compares it with the reference or set point (SP). The difference between actual and desired value of the process variable, called the ''error'' signal, or SP-PV error, is applied as feedback to generate a control action to bring the controlled process variable to the same value as the set point. Other aspects which are also studied are controllability and observability. Control theory is used in control system eng ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Control Theory Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any ''delay'', ''overshoot'', or ''steady-state error'' and ensuring a level of control stability; often with the aim to achieve a degree of optimality. To do this, a controller with the requisite corrective behavior is required. This controller monitors the controlled process variable (PV), and compares it with the reference or set point (SP). The difference between actual and desired value of the process variable, called the ''error'' signal, or SP-PV error, is applied as feedback to generate a control action to bring the controlled process variable to the same value as the set point. Other aspects which are also studied are controllability and observability. Control theory is used in control system eng ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Allen Tannenbaum Allen Robert Tannenbaum (born January 25, 1953) is an American/Israeli applied mathematician and presently Distinguished Professor of Computer Science and Applied Mathematics & Statistics at the State University of New York at Stony Brook. He is also Visiting Investigator of Medical Physics at Memorial Sloan Kettering Cancer Center in New York City. He has held a number of other positions in the United States, Israel, and Canada including the Bunn Professorship of Electrical and Computer Engineering and Interim Chair, and Senior Scientist at the Comprehensive Cancer Center at the University of Alabama, Birmingham. He received his B.A. from Columbia University in 1973 and Ph.D. with thesis advisor Heisuke Hironaka at the Harvard University in 1976. Tannenbaum has done research in numerous areas including robust control, computer vision, and biomedical imaging, having almost 500 publications. He pioneered the field of robust control with the solution of the gain margin and phase ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Rosenbrock System Matrix In applied mathematics, the Rosenbrock system matrix or Rosenbrock's system matrix of a linear time-invariant system is a useful representation bridging state-space representation and transfer function matrix form. It was proposed in 1967 by Howard H. Rosenbrock. Definition Consider the dynamic system :: \dot= Ax +Bu, :: y= Cx +Du. The Rosenbrock system matrix is given by ::P(s)=\begin sI-A & -B\\ C & D \end. In the original work by Rosenbrock, the constant matrix D is allowed to be a polynomial in s. The transfer function between the input i and output j is given by ::g_=\frac where b_i is the column i of B and c_j is the row j of C. Based in this representation, Rosenbrock developed his version of the PHB test. Short form For computational purposes, a short form of the Rosenbrock system matrix is more appropriate and given by ::P\sim\begin A & B\\ C & D \end. The short form of the Rosenbrock system matrix has been widely used in H-infinity methods in control theory, wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Linear Fractional Transformation In mathematics, a linear fractional transformation is, roughly speaking, a transformation of the form :z \mapsto \frac , which has an inverse. The precise definition depends on the nature of , and . In other words, a linear fractional transformation is a ''transformation'' that is represented by a ''fraction'' whose numerator and denominator are ''linear''. In the most basic setting, , and are complex numbers (in which case the transformation is also called a Möbius transformation), or more generally elements of a field. The invertibility condition is then . Over a field, a linear fractional transformation is the restriction to the field of a projective transformation or homography of the projective line. When are integer (or, more generally, belong to an integral domain), is supposed to be a rational number (or to belong to the field of fractions of the integral domain. In this case, the invertibility condition is that must be a unit of the domain (that is or in the c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Hardy Space In complex analysis, the Hardy spaces (or Hardy classes) ''Hp'' are certain spaces of holomorphic functions on the unit disk or upper half plane. They were introduced by Frigyes Riesz , who named them after G. H. Hardy, because of the paper . In real analysis Hardy spaces are certain spaces of distributions on the real line, which are (in the sense of distributions) boundary values of the holomorphic functions of the complex Hardy spaces, and are related to the ''Lp'' spaces of functional analysis. For 1 ≤ ''p'' < ∞ these real Hardy spaces ''H^p'' are certain subset s of ''L^p'', while for ''p'' < 1 the ''L^p'' spaces have some undesirable properties, and the Hardy spaces are much better behaved. There are also higher-dimensional generalizations, consisting of certain holomorphic functions on [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Proceedings Of The Royal Society A ''Proceedings of the Royal Society'' is the main research journal of the Royal Society. The journal began in 1831 and was split into two series in 1905: * Series A: for papers in physical sciences and mathematics. * Series B: for papers in life sciences. Many landmark scientific discoveries are published in the Proceedings, making it one of the most historically significant science journals. The journal contains several articles written by the most celebrated names in science, such as Paul Dirac, Werner Heisenberg, Ernest Rutherford, Erwin Schrödinger, William Lawrence Bragg, Lord Kelvin, J.J. Thomson, James Clerk Maxwell, Dorothy Hodgkin and Stephen Hawking. In 2004, the Royal Society began ''The Journal of the Royal Society Interface'' for papers at the interface of physical sciences and life sciences. History The journal began in 1831 as a compilation of abstracts of papers in the ''Philosophical Transactions of the Royal Society'', the older Royal Society publication, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	H Square In mathematics and control theory, ''H''2, or ''H-square'' is a Hardy space with square norm. It is a subspace of ''L''2 space, and is thus a Hilbert space. In particular, it is a reproducing kernel Hilbert space. On the unit circle In general, elements of ''L''2 on the unit circle are given by :\sum_^\infty a_n e^ whereas elements of ''H''2 are given by :\sum_^\infty a_n e^. The projection from ''L''2 to ''H''2 (by setting ''a''''n'' = 0 when ''n'' < 0) is orthogonal. On the half-plane The Laplace transform $\mathcal$ given by : $s)=\int_0^\infty e^f(t)dt$ can be understood as a linear operator : $\mathcal:L^2(0,\infty)\to H^2\left(\mathbb^+\right)$ where $L^2(0,\infty)$ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]

On the half-plane