2011
DOI: 10.2478/v10127-011-0018-0
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The estimation of the dynamics of indirect control switching systems

Abstract: ABSTRACT. The paper deals with the time switching hybrid systems described by nonlinear control equations with nonlinearity of a sector form. The estimation of the solution of the control system at any moment is established through the method of Lyapunov function. Both cases, stable and unstable control systems are considered. The final estimation of the solution of the hybrid system is obtained from the composition of perturbations of the separate control systems using the condition of solution continuity in … Show more

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Cited by 2 publications
(3 citation statements)
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“…Along with mutual authentication, encryption and integrity keys are generated [12]. At the same time, the principle of cryptography (Kirchhoff's principle) is fulfilled in limiting the duration of using a permanent key to a minimum and using temporary keys [13]. The authentication procedure starts after the user is identified in the serving network by the procedure for ensuring the privacy of the location of the mobile station [16].…”
Section: Researches Methodologymentioning
confidence: 99%
“…Along with mutual authentication, encryption and integrity keys are generated [12]. At the same time, the principle of cryptography (Kirchhoff's principle) is fulfilled in limiting the duration of using a permanent key to a minimum and using temporary keys [13]. The authentication procedure starts after the user is identified in the serving network by the procedure for ensuring the privacy of the location of the mobile station [16].…”
Section: Researches Methodologymentioning
confidence: 99%
“…where Θ denotes the zero matrix, and the expression inside denotes that the relevant matrix is positive definite. Since, in view of the vector and matrix norms defined by (5) and 7, we have X(t) = x(t) , thus the total derivative of the Lyapunov function can be estimated as…”
Section: Systems With the Quadratic Right-hand Sidementioning
confidence: 99%
“…As a method of investigation such systems, the second Lyapunov method with quadratic Lyapunov functions is used [2]. The second Lyapunov method using the Lyapunov function of Lurje-Postnikov type was used in [5] to obtain an estimation of a solution to a control equation with nonlinearity of a sector form.…”
Section: Introductionmentioning
confidence: 99%