Features

Solutions of the Lyapunov and Sylvester Matrix Equations

• Schur methods for solving the Lyapunov equations

• Hessenberg-Schur methods for solving the Sylvester equations

• Direct computation of the Cholesky factors of the controllability and observability Gramians

Solutions of the Algebraic Riccati Equations

• Schur, Newton's, and matrix-sign methods for solving the discrete and continuous matrix algebraic Riccati equations

• Inverse-free methods based on the generalized eigenvector and the generalized Schur decompositions

Reduction to Controller-Hessenberg and Observer-Hessenberg Forms

• Computation of the block controller-Hessenberg and observer-Hessenberg forms

Controllability and Observability Tests

• Controllability and observability tests using the controller-Hessenberg and observer-Hessenberg forms

• Controllability and observability tests using the Cholesky factors of the controllability and observability Gramians

Pole Assignment

• Recursive, explicit QR, and Schur methods for multi-input systems

• RQ modification of the recursive method and the implicit RQ method for single-input systems

• Projection technique for the partial pole assignment problem

Feedback Stabilization

• Pole assignment algorithms for feedback stabilization with constraints on the damping factor, settling time, damping ratio, and natural frequency

• Lyapunov shift and partial Lyapunov shift algorithms for feedback stabilization

Design of the Reduced-Order State Estimator (Observer)

• Reduced-order state estimator design using the pole assignment approach

• Reduced-order state estimator design using the recursive triangular, the block recursive triangular, the recursive bidiagonal, and the block recursive bidiagonal algorithms for solving the Sylvester-observer equation

Model Reduction

• Schur and square-root methods for selecting the dominant subsystem and model reduction

Model Identification

• System identification from the impulse responses, frequency responses, and generic input-output data

Miscellaneous Matrix Decompositions and Functions

• Computation of the generalized eigenvalues, generalized eigenvectors, and generalized Schur decomposition

• Computation of the ordered generalized Schur decomposition