Journal ArticleDOI
Time-varying version of the lemma of Lyapunov
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TLDR
In this article, the lemma of Lyapunov is generalized for time-varying systems, in which it is shown that additional conditions are required for the lemmas to hold.Abstract:
The lemma of Lyapunov gives the necessary and sufficient condition for the stability of a time-invariant system in terms of the existence of a positive-definite symmetric matrix. In this letter, the lemma is generalised for time-varying systems, in which it is shown that additional conditions are required for the lemma to hold. The conditions involve boundedness of certain quantities and uniform complete observability of a pair of matrixes.read more
Citations
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Journal ArticleDOI
Linear time-variable systems: Balancing and model reduction
TL;DR: In this article, a "uniformly balanced" realization for linear time-variable systems is defined, characterized by the fact that its controllability and observability Gramians are equal and diagonal.
Journal ArticleDOI
Stability properties of Kalman-Bucy filters
TL;DR: In this paper, conditions for Kalman-Bucy filters were found guaranteeing asymptotic stability, but not necessarily uniform stability, with respect to complete controllability conditions.
Journal ArticleDOI
On the Stability of Kalman--Bucy Diffusion Processes
TL;DR: The Kalman-Bucy filter has been studied extensively in the literature since the seminal 1961 paper of Kalman and Bucy as mentioned in this paper, and it is generally the only finite-dimensional exact instance of the Bayes filter for continuous state-space models.
Journal ArticleDOI
Stability, observability and invariance
TL;DR: In this article, observability-type considerations and invariance principle are shown to complement each other in the study of the asymptotic behavior and stability of differential equations, and applications to stabilization and identification follow.
Journal ArticleDOI
A New Iterative Algorithm to Solve Periodic Riccati Differential Equations With Sign Indefinite Quadratic Terms
TL;DR: In this paper, an iterative algorithm to solve periodic Riccati differential equations (PRDE) with an indefinite quadratic term is proposed and the global convergence and the local quadRatic rate of convergence are established.
References
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Contributions to the theory of optimal control
TL;DR: In this article, the authors considered the problem of least square feedback control in a linear time-invariant system with n states, and proposed a solution based on the concept of controllability.
BookDOI
Linear system theory
TL;DR: In this paper, the main thrusts of the work are the analysis of system descriptions and derivations of their properties, LQ-optimal control, state feedback and state estimation, and MIMO unity-feedback systems.