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Explicit Stability Conditions for Continuous Systems [electronic resource] : A Functional Analytic Approach / by Michael I. Gil.

By: Gil, Michael I [author.]Contributor(s): SpringerLink (Online service)Material type: TextTextSeries: Lecture Notes in Control and Information Sciences ; 314Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2005Edition: 1st ed. 2005Description: X, 190 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540316374Subject(s): Control engineering | Robotics | Mechatronics | Vibration | Dynamical systems | Dynamics | System theory | Statistical physics | Control, Robotics, Mechatronics | Vibration, Dynamical Systems, Control | Systems Theory, Control | Complex Systems | Statistical Physics and Dynamical SystemsAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 629.8 LOC classification: TJ210.2-211.495TJ163.12Online resources: Click here to access online
Contents:
Preliminaries -- Perturbations of Linear Systems -- Linear Systems with Slowly Varying Coefficients -- Linear Dissipative and Piecewise Constant Systems -- Nonlinear Systems with Autonomous Linear Parts -- The Aizerman Problem -- Nonlinear Systems with Time-Variant Linear Parts -- Essentially Nonlinear Systems -- The Lur'e Type Systems -- The Aizerman Type Problem for Nonautonomous Systems -- Input - State Stability -- Orbital Stability and Forced Oscillations -- Positive and Nontrivial Steady States.
In: Springer eBooksSummary: Explicit Stability Conditions for Continuous Systems deals with non-autonomous linear and nonlinear continuous finite dimensional systems. Explicit conditions for the asymptotic, absolute, input-to-state and orbital stabilities are discussed. This monograph provides new tools for specialists in control system theory and stability theory of ordinary differential equations, with a special emphasis on the Aizerman problem. A systematic exposition of the approach to stability analysis based on estimates for matrix-valued functions is suggested and various classes of systems are investigated from a unified viewpoint.
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Preliminaries -- Perturbations of Linear Systems -- Linear Systems with Slowly Varying Coefficients -- Linear Dissipative and Piecewise Constant Systems -- Nonlinear Systems with Autonomous Linear Parts -- The Aizerman Problem -- Nonlinear Systems with Time-Variant Linear Parts -- Essentially Nonlinear Systems -- The Lur'e Type Systems -- The Aizerman Type Problem for Nonautonomous Systems -- Input - State Stability -- Orbital Stability and Forced Oscillations -- Positive and Nontrivial Steady States.

Explicit Stability Conditions for Continuous Systems deals with non-autonomous linear and nonlinear continuous finite dimensional systems. Explicit conditions for the asymptotic, absolute, input-to-state and orbital stabilities are discussed. This monograph provides new tools for specialists in control system theory and stability theory of ordinary differential equations, with a special emphasis on the Aizerman problem. A systematic exposition of the approach to stability analysis based on estimates for matrix-valued functions is suggested and various classes of systems are investigated from a unified viewpoint.

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