Title :
Balanced truncation of linear time-varying systems
Author :
Sandberg, Henrik ; Rantzer, Anders
Author_Institution :
Dept. of Autom. Control, Lund Inst. of Technol., Sweden
Abstract :
In this paper, balanced truncation of linear time-varying systems is studied in discrete and continuous time. Based on relatively basic calculations with time-varying Lyapunov equations/inequalities we are able to derive both upper and lower error bounds for the truncated models. These results generalize well-known time-invariant formulas. The case of time-varying state dimension is considered. Input-output stability of all truncated balanced realizations is also proven. The method is finally successfully applied to a high-order model.
Keywords :
Lyapunov matrix equations; continuous time systems; discrete time systems; input-output stability; invariance; linear systems; observability; reachability analysis; reduced order systems; time-varying systems; Lyapunov equations; Lyapunov inequalities; balanced truncation; continuous time; discrete time; error bound; high-order model; input-output stability; linear time-varying systems; model reduction; observability; reachability; state-dimension; time-invariant formulas; Asymptotic stability; Councils; Linear approximation; Linear systems; Nonlinear systems; Reduced order systems; Riccati equations; Robust control; Sufficient conditions; Time varying systems;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2003.822862
