Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.245: MULTIVARIABLE CONTROL SYSTEMS
by A. Megretski
Problem Set 8 Solutions
1
Problem 8.1
For the standard LTI feedback design setup defined by equations
x(t)
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.245: MULTIVARIABLE CONTROL SYSTEMS
by A. Megretski
Problem Set 7 Solution
1
Problem 7.1
(a) A state-space representation for this problem is given by
x
z1
z2
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.245: MULTIVARIABLE CONTROL SYSTEMS
by A. Megretski
Problem Set 5 Solutions
1
Problem 5.1
Use KYP Lemma to find (analytically) the set of all a R such that th
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.245: MULTIVARIABLE CONTROL SYSTEMS
by A. Megretski
Problem Set 4 Solution
1
Problem 4.1
For the SISO feedback design from Figure 4.1, where it is known that
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.245: MULTIVARIABLE CONTROL SYSTEMS
by A. Megretski
Problem Set 3 Solutions
1
Problem 3.1
Consider a control system described by
q (t) a2 q (t) = v (t) + f1 (
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.245: MULTIVARIABLE CONTROL SYSTEMS
by A. Megretski
Problem Set 2 Solutions
1
Problem 2.1
For each of the statements below decide whether it is true or false.
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.245: MULTIVARIABLE CONTROL SYSTEMS
by A. Megretski
Problem Set 1 Solutions
1
Problem 1.1
Consider the task of finding a controller F = F (s) (with two inputs
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.245: MULTIVARIABLE CONTROL SYSTEMS
by A. Megretski
Analysis of Uncertain Systems1
In this lecture enhanced techniques of stability and robustness analysis of
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.245: MULTIVARIABLE CONTROL SYSTEMS
by A. Megretski
Convex Optimization1
Many optimization objectives generated by LTI system design and analysis do not t
wit
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.245: MULTIVARIABLE CONTROL SYSTEMS
by A. Megretski
The Tustin Transform1
So far, the optimization methods under consideration were presented for the continuo
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.245: MULTIVARIABLE CONTROL SYSTEMS
by A. Megretski
Q-Parameterization1
This lecture introduces the so-called Q-Parameterization (sometimes referred to as the
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.245: MULTIVARIABLE CONTROL SYSTEMS
by A. Megretski
Hankel Optimal Model Order Reduction1
This lecture covers both the theory and an algorithmic side of Hanke
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.245: MULTIVARIABLE CONTROL SYSTEMS
by A. Megretski
Fundamentals of Model Order Reduction1
This lecture introduces basic principles of model order reduction f
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.245: MULTIVARIABLE CONTROL SYSTEMS
by A. Megretski
Kalman-Yakubovich-Popov Lemma
1
A simplied version of KYP lemma was used earlier in the derivation of opti
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.245: MULTIVARIABLE CONTROL SYSTEMS
by A. Megretski
The Waterbed Eect1
A common eect, usually associated with unstable zeroes and poles of the open loop
plant
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.245: MULTIVARIABLE CONTROL SYSTEMS
by A. Megretski
Using H2 Optimization1
This lecture provides some useful hints on ways to apply H2 optimization.
4.1
Close
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.245: MULTIVARIABLE CONTROL SYSTEMS
by A. Megretski
Solving the H2 optimization problem1
There are several ways to derive a solution to the H2 optimization pr
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.245: MULTIVARIABLE CONTROL SYSTEMS
by A. Megretski
Interpretations for Standard Optimization Setup1
This is the second lecture on standard feedback optimizat
Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.245: MULTIVARIABLE CONTROL SYSTEMS
by A. Megretski
Standard LTI Feedback Optimization Setup1
The two most frequently used techniques of optimization-based fe