Compute estimator gains for a continuous-time system:

A discrete-time system:

Estimator gains for a two-output system with only the second output measured:

A set of gains for a SISO system:

Verify the solution:

An observer gain matrix for a two-output system:

Estimator gain matrix for a three-output system with specified measurements:

Compute the estimator gains with poles specified as the roots of a polynomial:

Determine estimator gains symbolically:

Compute the gains for an AffineStateSpaceModel:

Assemble the estimator:

The estimator poles are at the desired location:

Construct an observer for a continuous-time system:

Simulate the system with input Sin[t] and from a random initial condition:

Compare each state and its estimate:

Construct an observer for a zero-input sampled-data system:

Compute the actual and estimated states for initial states {1,–0.75,0.5} and initial observer states {0,0,0}:

Examine the state tracking achieved by the observer:

The error dynamics:

StateOutputEstimator assembles an observer that estimates both the states and outputs:

The prediction estimator dynamics for a discrete-time system:

Estimator gains are the conjugate transpose of state feedback gains of the dual system:

Or vice versa:

For an observable, nonsingular descriptor system, all the estimator poles can be placed:

For a singular system that is observable, only MatrixRank[e] poles can be placed:

An impulsive system where only the slow subsystem is observable:

Only the estimator pole for the slow system can be placed:

The KNVD method does not handle exact systems with fewer outputs than states:

Evaluate numerically:

The KNVD method does not support a pole multiplicity greater than the number of outputs:

Use the Ackermann method:

The KNVD method can give different sets of gains on different computer systems:

The observer's eigenvalues are the same:

The system must be observable:

It is not observable: