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Stabilization of Linear Systems by Noise
SIAM Journal on Control and Optimization, 1983It is proved that the biggest Lyapunov number $\lambda _{\max } $ of the system $\dot x = (A + F(t))x$, where A is a fixed $d \times d$ matrix and $F(t)$ is a zero mean strictly stationary matrix-valued stochastic process, satisfies ${1 / d}$ trace $A \leqq \lambda _{\max } $.
Arnold, Ludwig +2 more
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Stabilization of switched linear systems
IEEE Transactions on Automatic Control, 2005In this note, we study the stabilization problem of systems that switch among a finite set of controllable linear systems with arbitrary switching frequency. For both cases of known and unknown switching functions, feedback laws are designed to achieve exponential stability.
Daizhan Cheng +3 more
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On stabilization of switched linear systems
Systems & Control Letters, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zvi Artstein, Jonathan Ronen
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Stabilization of Uncertain Linear Systems [PDF]
, 1991 Feedback stabilization of linear, uncertain systems is usually analyzed using quadratic Lyapunov functions that are common to all values in the uncertainty set. In this paper we use the alternative classical concept of Laypunov exponents to characterize the precise (exponential) stability regions for systems with contrained linear output feedback.
Colonius, Fritz, Kliemann, Wolfgang
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Stability of Linear Positive Systems
Ukrainian Mathematical Journal, 2001The author considers the linear system \[ \dot H+MH=G(t),\quad t\geq 0,\tag{1} \] where \(M:\mathcal{E} \mapsto \mathcal{E}\) is a bounded operator in a Banach space \(\mathcal{E}\), which has the structure of a partially ordered space with respect to a fixed cone \(\mathcal{K}\subset\mathcal{E}\).
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Stability Constants in Linear Spaces
Constructive Approximation, 2010Let \(X\) be a linear space over the reals, \(D\subset X,\) and let \(E\) be a Banach space. A function \(f:D\to E\) is said to be \(\delta\)-Jensen if \[ \left\| f\left(\frac{x+y}{2}\right)-\frac{f(x)+f(y)}{2}\right\|\leq\delta \] whenever \(x,y,(x+y)/2\in D.\) The stability constant for Jensen equation is the infimum of those constants \(C\) for ...
Laczkovich, M., Paulin, R.
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Notes on the Stability of Linear Networks
Proceedings of the IRE, 1944Not ...
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Stabilization of positive linear systems
Systems & Control Letters, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Patrick De Leenheer, Dirk Aeyels
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STABILIZATION OF LINEAR DISTRIBUTED SYSTEMS
IFAC Proceedings Volumes, 1983Abstract The problem of shifting a finite set of eigenvalues to predetermined points on the complex plane in infinite dimensional systems is considered. Basing on that a stabilization method is given for systems in which the unstable subspace of the state space is finite dimensional.
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