this is a review from cmu refer
state variable method
any Nth order differential equation describing a control system could be reduced to N 1st order equations, these equations could be arranged in the form of matrix equations.
define x as system state, y as output, u as input:
modern control methods(ODEs) can handle multiple-input-multiple-outputs, and they can be optimized, and they allow to design performance and cost model.
effects of uncertainty
observability
the ability to observe all of the parameters or state variables in the system
controllability
the ability to move a system from any given state to any desired state
stability
the bounded response to any bounded input
robust control theory might be stated as a worst-case analysis, to bound the uncertantiy.
metircs
how to model the behavior of the test system is one most difficult challenge in design a good control system.
adaptive control
set up observers for each significant state variable. at each iteration loop, the system learns about the changes in the system parameters, and getting closer to the desired. while the method may suffer from convergence issues
H2 or H-infinity
H2 control seeks to bound the power gain of the system, H-infinity seeks to bound the energy gain of the system. gains in power or energy indicate operation of the system near a pole in the transfer function.
parameter estimation
by establishing boundaries in the frequency domain that cannot be crossed to maintain stability.
Lyapanov
the only universal tech for assessing non-linear systems, the method focus on stability. Lyapanov functions are constructed, which are described as energy-like functions, to model the behavior of real system.