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Decomposition of Linear Systems on Disconnected Lie Groups
This manuscript studies the global dynamics of a linear system on a disconnected Lie group. It shows that the connected components of the equilibria...
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Discrete Linear Systems
In Chap. 4 , we considered the dynamics of single quantities changing in either discrete or...
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Controllability of periodic linear systems, the Poincaré sphere, and quasi-affine systems
For periodic linear control systems with bounded control range, an autonomized system is introduced by adding the phase to the state of the system....
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Sensitivity-Driven Experimental Design to Facilitate Control of Dynamical Systems
Control of nonlinear dynamical systems is a complex and multifaceted process. Essential elements of many engineering systems include high-fidelity...
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Measure and Statistical Attractors for Nonautonomous Dynamical Systems
Various inequivalent notions of attraction for autonomous dynamical systems have been proposed, each of them useful to understand specific aspects of...
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Auxiliary Functions as Koopman Observables: Data-Driven Analysis of Dynamical Systems via Polynomial Optimization
We present a flexible data-driven method for dynamical system analysis that does not require explicit model discovery. The method is rooted in...
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Partial Stability of Systems of Itô Linear Delay Differential Equations
AbstractWe study the moment stability of solutions in part of the variables with respect to the initial data for systems of Itô linear delay...
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Cascade Super-Twisting Observer for Linear Multiagent Systems without Communication
AbstractThe paper addresses the consensus problem (i.e., the agreement of state vectors) for a multiagent system consisting of identical linear...
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Homoclinic Orbits and Chaos in Nonlinear Dynamical Systems: Auxiliary Systems Method
AbstractThe auxiliary systems method in other words the method of two-dimensional comparison systems plays an essential role in the nonlocal...
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Coding and Control for Linear Gaussian Systems: Separation, Optimality and Linearity
In the previous chapter, we obtained the structure of optimal encoders for general stochastic, controlled and control-free, dynamical systems. Due to...
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Generalized Markov–Bernstein Inequalities and Stability of Dynamical Systems
AbstractWe analyze the Markov–Bernstein type inequalities between the norms of functions and of their derivatives for complex exponential...
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Transformations of the matrices of the fractional linear systems to their canonical stable forms
A new approach to the transformations of the matrices of the fractional linear systems with desired eigenvalues is proposed. Conditions for the...
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Periodic orbits for 2n-dimensional control piecewise smooth dynamical systems
In this paper we study the periodic orbits of a class of 2 n -dimensional control dynamical systems with a perturbation of continuous piecewise smooth...
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On the Poincaré–Bendixson Index Theorem for a Class of Piecewise Linear Differential Systems
Poincaré–Bendixson index theorem showed that: if planar smooth differential systems have only finitely number of singular points inside a limit...
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Adaptive Observer of State and Disturbances for Linear Overparameterized Systems
AbstractThe problem of state reconstruction is considered for a class of linear systems with time-invariant unknown parameters and...
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Relative controllability of linear state-delay fractional systems
In this paper, our focus is on exploring the relative controllability of systems governed by linear fractional differential equations incorporating...
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Discrete Dispersive Dynamical Systems
In this chapter we study turnpike properties for a discrete dispersive dynamical system generated by set-valued map**s, which was introduced by A....
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Limit cycles of multi-parameter polynomial dynamical systems
This is an overview of our recent works on the global bifurcation analysis of multi-parameter polynomial dynamical systems. In particular, using our...
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On stable solution of the problem of disturbance reduction in a linear dynamical system
We study the problem of active reduction of the influence of a disturbance on the output of a linear controlled system. The problem is studied on a...
