Bellman-Gronwall Inequality Approach to Oscillator Design for the Specific Bilinear Systems

Bellman-Gronwall Inequality Approach to Oscillator Design for the Specific Bilinear Systems

In this paper, the existence of limit cycles for the specific bilinear systems is explored. Based on the BellmanGronwall inequality approach, not only the exponentially stable limit cycles phenomenon of such systems can be certified but also the oscillation behaviors of such systems can be correctly predicted. Finally, a numerical example is provided to illustrate the feasibility and effectiven...

A New Generalized Gronwall-Bellman Type Inequality

Finite-time stability analysis of fractional order time delay systems: Bellman-Gronwall`s approach

The paper extends some basic results from the area of finite time and practical stability to nonlinear , perturbed , fractional order time-delay systems where a robust stability test procedure is proposed. The problem of sufficient conditions that enable system trajectories to stay within the a priori given sets for the particular class of nonlinear fractional order time delay systems is examin...

Fractional difference inequalities of Gronwall – Bellman type

Discrete inequalities, in particular the discrete analogues of the Gronwall–Bellman inequality, have been extensively used in the analysis of finite difference equations. The aim of the present paper is to establish some fractional difference inequalities of Gronwall–Bellman type which provide explicit bounds for the solutions of fractional difference equations.

A Generalized Gronwall–bellman Type Delay Integral Inequality with Two Independent Variables on Time Scales

Using a technique of monotonization, this paper investigates a generalized GronwallBellman type delay integral inequality with two independent variables on time scales. The result not only unifies some continuous inequalities and their discrete analogues but also extends some known integral inequalities on time scales. An application to the estimation of solutions of delay dynamic integral equa...