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Linear Systems
This chapter deals with linear systems of ordinary differential equations (ODEs), both homogeneous and nonhomogeneous equations. Linear systems are...
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On Trajectories of Dynamic Systems Lying on Hypersurfaces of Linear Systems
Abstract —Lagutinskii’s theory of integration of dynamic systems is reformulated for arbitrary linear systems of hypersurfaces. The following problems...
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Reduction of Schlesinger Systems to Linear Jordan–Pochhammer Systems
We study the reducibility of an isomonodromic family of Fuchsian systems on the Riemann sphere which is determined by some initial Fuchsian system...
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Homogeneous Linear Systems
In the important special case where \(t\mapsto A(t) \) is a...
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A Note on Quaternion Linear Dynamical Systems
We established conditions of stability and instability of quaternion linear dynamical systems, linear differential and linear fractional equations.
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Linear Time-Varying Systems
In this chapter we consider linear time-varying (LTV) systems. These are systems whose behaviour depends on the particular moment in time at which...
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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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Prescribed-time leader-following consensus of linear multi-agent systems by bounded linear time-varying protocols
This paper considers the prescribed-time leader-following consensus problem of input-constrained linear multi-agent systems under generally directed...
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Possibilities in Linear Inequality Systems
Knowledge of solvability of linear inequality systems is indispensable for discussing constrained optimization problems, which is one of the subjects...
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Linear Time Invariant Systems
We assume the reader to have familiarity with linear time-invariant (LTI) systems. In this chapter we merely summarise the main results of this...
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Monotone Linear Dynamical Systems over Dioids
Linear systems over naturally ordered dioids are other kinds of positive systems than the usual ones over semiring (...
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Indefinite Linear Quadratic Optimal Control Problem for Continuous-time Linear Descriptor Markov Jump Systems
The indefinite linear quadratic (ILQ) optimal control problem for continuous-time descriptor Markov jump systems (DMJSs) is discussed in this work....
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Robust Stability of Linear Delay Systems with Unknown Parameters
AbstractThis note is concerned with the stability of linear delay systems. We investigate the robust stability of the delay systems with unknown...
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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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Practical RPCG methods for complex symmetric linear systems
We investigate the restrictively preconditioned conjugate gradient (RPCG) method for complex symmetric linear systems. First, we transform the...
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Nonlinear Control of Linear Systems
Chapter 4 of the book Nonlinear Systems and Controls describes nonlinear controls for linear controlled systems. Among other elements, these include...
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Data-driven discovery of linear dynamical systems from noisy data
In modern science and engineering disciplines, data-driven discovery methods play a fundamental role in system modeling, as data serve as the...
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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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Systems of Linear Equations
One of the most important problems in linear algebra is solving systems of linear equations. This chapter takes a closer look at them.Linear system
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Interval Reduced-order Switched Positive Observers for Uncertain Switched Positive Linear Systems
In this paper, existence conditions and a design procedure of reduced-order switched positive observers for continuous- and discrete-time switched...