Automatica (Journal of IFAC)
ACM Transactions on Mathematical Software (TOMS)
Matrix computations (3rd ed.)
Disturbance Decoupling for Descriptor Systems by State Feedback
SIAM Journal on Control and Optimization
Observers for Linear Systems
Computer-Aided Control System Design
Computer-Aided Control System Design
On the Computation of the Restricted Singular Value Decomposition via the Cosine-Sine Decomposition
SIAM Journal on Matrix Analysis and Applications
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In this paper, matrix pencil theory is used to study the squaring-down problem where a linear time-invariant system with an unequal number of inputs and outputs is turned into an invertible square system with an equal number of inputs and outputs. Both static and dynamic compensators are considered for squaring down. In the case of static compensation, the infinite-zero structure of the original system is preserved after squaring down. In the case of dynamic compensation, key system properties including stabilizability, detectability and the infinite-zero structure of the original system are also preserved after squaring down. Furthermore, one can additionally assign the invariant zeros induced by squaring down to the open left half plane, provided that the original system is stabilizable and detectable. This means that squaring down by dynamic compensation preserves minimum phaseness as well. The preservation of these system properties is highly desirable for subsequent feedback design of the squared-down system. Unlike existing squaring-down methods which do not address the issue of numerical properties, our solution is based on a condensed form derived using only orthogonal transformations which are numerically stable. Explicit formulas which can be implemented in a numerically reliable manner are given for determining the squaring-down compensators. Examples are presented to illustrate the numerical superiority of the proposed method.