EstimatorGains

A set of gains for a SISO system:

Verify the solution:

An observer gain matrix for a two-output system:

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

Determine estimator gains symbolically:

The Ackermann method is used by default for systems with exact values:

For inexact systems with multiple output channels, the Ackermann method selects the output channel for which the observability matrix has the smallest condition number:

The second output has the lower condition number:

The gains associated with the first output:

The KNVD method uses all available outputs to estimate the states:

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 and initial observer states :

Examine the state tracking achieved by the observer:

The error dynamics:

The observer dynamics:

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

The estimator gains are the conjugate transpose of the state feedback gains of the dual system:

Or vice versa:

The KNVD method does not handle exact systems when the number of measurements is less than the number of states:

Evaluate numerically:

The KNVD method cannot handle cases in which the multiplicity of the poles exceeds the number of measurements:

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: