6 . 245 : Multivariable Control Systems
نویسنده
چکیده
Let M be a complex matrix of rank one, i.e. M = pq′ where p, q are complex nby-1 matrices and ′ denotes Hermitean conjugation. Let μC(M) and μR(M) denote the structured singular values μ(M,∆) of M defined with ∆ = ∆C and ∆ = ∆R respectively, where ∆C is the cone of all diagonal matrices with complex entries, and ∆R is the cone of all diagonal matrices with real entries. (a) Express μC(M) and μR(M) as elementary functions of the components pi and qi of p and q (i.e. using the elementary operations of multiplication, addition, maximum of n numbers, division, trigonometric, exponential, etc.).
منابع مشابه
Optimal Control of Nonlinear Multivariable Systems
This paper concerns a study on the optimal control for nonlinear systems. An appropriate alternative in order to alleviate the nonlinearity of a system is the exact linearization approach. In this fashion, the nonlinear system has been linearized using input-output feedback linearization (IOFL). Then, by utilizing the well developed optimal control theory of linear systems, the compensated ...
متن کاملControl of Multivariable Systems Based on Emotional Temporal Difference Learning Controller
One of the most important issues that we face in controlling delayed systems and non-minimum phase systems is to fulfill objective orientations simultaneously and in the best way possible. In this paper proposing a new method, an objective orientation is presented for controlling multi-objective systems. The principles of this method is based an emotional temporal difference learning, and has a...
متن کاملScience 6 . 245 : MULTIVARIABLE CONTROL SYSTEMS
So far, the optimization methods under consideration were presented for the continuous time case. This lecture describes a technique which allows one to apply the continuous time algorithms of H2 optimization, H-Infinity optimization, and Hankel optimal model reduction to discrete time systems. The technique is based on applying the familiar “Tustin” (or “bilinear”) CT to DT transformation. Whi...
متن کامل6 . 245 : MULTIVARIABLE CONTROL SYSTEMS by A . Megretski Hankel Optimal Model Order Reduction
9.1.1 The Optimization Setup Let G = G(s) be a matrix-valued function bounded on the jθ-axis. The task of Hankel ˆ optimal model reduction of G calls for finding a stable LTI system G of order less than a given positive integer m, such that the Hankel norm ∞�∞H of the difference � = G − Ĝ is minimal. Remember that Hankel norm of an LTI system with transfer matrix � = �(s), input w, and output v...
متن کامل