At the completion of EE611, you should be able to perform the following objectives:

• Do all EE421 and EE422 objectives
• Solve Ax=b using gaussian elimination
• Find A^-1
• Determine the orthogonality of vectors
• Understand fields and vector spaces
• Understand the notions of span, basis, rank, and dimension
• Understand the meaning of domain, codomain, range, onto, into, image, and one-to-one as they apply to functions and transformations.
• Determine if a function (transformation) has an inverse
• Understand and apply the concepts of linear transformation and null space.
• Find the eigenvalues, eigenvectors, and possibly generalized eigenvectors of a matrix
• Define and apply the concept of degeneracy
• Prove simple facts about matrices and eigenvalues
• Use eigenvectors to decouple quadratic forms
• Apply theorems concerning convergence of power series of scalar and matrix functions
• Prove simple identities involve matrix power series
• Understand the origin of Jordan blocks and find e^Jt
• Understand and apply the Cayley-Hamilton Theorem
• Evaluate e^At using three different methods
• Evaluate e^At for block diagonal matrices
• Find state variable models from input-output differential equations
• Find state variable models from transfer functions using three different methods
• Find state variable models from physical systems (circuits)
• Find a similarity transformation which decouples a state variable model
• Understand the concept of state variables
• Derive the state transition matrix and the solution to the state equation for linear, time-invariant systems
• Derive the four important properties of the state transition matrix forlinear, time-varying systems
• Define controllability and observability from a decoupled mode point of view
• Determine uncontrollable and controllable eigenvalues for single-input systems (either continuous or discrete).
• Define controllability in terms of using feedback to alter closed-loop eigenvalues
• Determine an appropriate eigenvalue assignment to meet transient specifications.
• Design a feedback regulator to assign the eigenvalues of a single-input controllable system
• Understand and apply the concept of a cyclic matrix for multi-input systems
• Design a feedback regulator to assign the eigenvalues of a multi-input controllable system

• Do all Exam I objectives!
• Determine uncontrollable and controllable eigenvalues for single-input systems (either continuous or discrete).
• Determine an appropriate eigenvalue assignment to meet transient specifications (either continuous or discrete).
• Design a feedback regulator law to assign the eigenvalues of a single-input controllable system (either continuous or discrete).
• Design a feedback control law so that system output achieves desired steady-state value (either continuous or discrete).
• Understand and apply the concept of a cyclic matrix
• Design a feedback control law to assign the eigenvalues of a multi-input controllable system (either continuous or discrete).
• Determine uncontrollable and controllable eigenvalues for multi-input systems (either continuous or discrete).
• Define and understand the concept of stabilizability (either continuous or discrete).
• Design a feedback control law to assign the controllable eigenvalues of a multi-input uncontrollable system.
• Determine observable and unobservable eigenvalues for single-input systems (either continuous or discrete).
• Design a full-order observer to estimate the states of multi-output observable systems (continuous).
• Determine observable and unobservable eigenvalues for multi-input systems (either continuous or discrete).
• Define and understand the concept of detectability (either continuous or discrete).
• Design a reduced-order observer to estimate the states of multi-input detectable systems (continuous).
• Prove the separation principle
• Define controllability and observability for time-varying continuous systems.
• Define and evaluate the controllability and observability grammian for time-varying systems (continuous).
• Design an open-loop control which will drive an initial state of a controllable, time-varying system to any other state in some finite time (continuous).
• Use two methods to obtain a discrete state variable model from a continuous state variable model.
• Find block diagram simulations of discrete state variable models and transfer functions.
• Define and evaluate the discrete state transition matrix, .
• Prove the identity and semi-group properties for .
• Solve the discrete state variable using time-domain and frequency domain techniques. Define and design deadbeat discrete systems.
• Solve the discrete state variable using time-domain and frequency domain techniques.
• Define and design deadbeat discrete systems.

• Define Markov parameters and Hankel matrices and use them to perform system identification of discrete-time systems
• Find the gradient, Jacobian, and the Hessian of nonlinear systems
• Linearize nonlinear systems about a nominal trajectory using perturbation theory
• Determine equilibrium points of nonlinear continuous and discrete systems
• Determine the stability of these equilibrium points using the direct method of Lyapunov
• Understand and apply Kravoskii's Method to determine the stability of nonlinear systems
• Determine the controllability and observability of nonlinear systems
• Transform controllable nonlinear systems into (nonlinear) controllable canonical form
• Design nonlinear regulators for nonlinear systems in (nonlinear) controllable canonical form.
• Transform observable nonlinear systems into (nonlinear) observable canonical form
• Design nonlinear observers for nonlinear systems in (nonlinear) observerable canonical form.