At the end of this course, the students will be able to

- interpret and apply the basic concepts of state space representation of multi-input multi-output (MIMO) dynamical systems, including
- the concept of state
- state and output equations
- state controllability, state observability, output controllability
- various state space representations for linear systems such as controllable canonical form, observable canonical form, diagonal canonical form and Jordan canonical form
- decomposition of systems and minimal realizations
- resolvent matrix and transfer function matrix
- linear transformation between various state space representations
- modal transformation;

- correlate the time response of a linear system and its state transition matrix;
- derive the state transition matrix of for a given system matrix;
- obtain the time response of a time invariant or time varying MIMO system to a specified set of inputs and initial conditions, using its state transition matrix;
- determine all equilibria for a given nonlinear system;
- demonstrate their understanding of various stability definitions;
- analyze the stability of a linear or nonlinear system about an equilibrium point using Lyapunov approach;
- design linear state feedback controllers, for the purpose of
- pole assignment using state feedback,
- decoupling via state feedback,
- obtaining optimal feedback coefficients for linear quadratic regulators;

- design state observers, including
- full order observers
- reduced order observers.