Correctness of many hybrid and distributed systems require stability and convergence guarantees. Unlike the standard induction principle for verifying invariance, a theory for verifying stability or convergence of automata is currently not available. In this paper, we formalize one such theory proposed by Tsitsiklis [25]. We build on the existing PVS metatheory for untimed, timed, and hybrid in...

A novel nonlinear fractional order sliding mode controller is proposed to control the chaotic atomic force microscope system in presence of uncertainties and disturbances. In the design of the suggested fractional order controller, conformable fractional order derivative is applied. The stability of the scheme is proved by means of the Lyapunov theory based on conformable fractional order deriv...

Abstract. A local convergence rate is established for a Gauss orthogonal collocation method applied to optimal control problems with control constraints. If the Hamiltonian possesses a strong convexity property, then the theory yields convergence for problems whose optimal state and costate possess two square integrable derivatives. The convergence theory is based on a stability result for the ...

The purpose of this paper is to provide the convergence theory for the iterative approach given by Chu [SIAM J. Numer. Anal.,29 (1992), pp. 885–903] in the context of solving inverse singular value problems. We give a detailed convergence analysis and investigate the ultimate rate of convergence. Numerical results which confirm our theory are presented.

1. BASIC PROBABILITY THEORY 1.1 Measure-theoretical foundation of probability theory 1.2 Independence 1.3 Borel measurable functions 1.4 Mathematical expectatlon 1.5 Characteristic functions 1.6 Random functions 2. CONVERGENCE 2.1 Heak and strong convergence of random variables 2.2 Convergence of mathematical expectations 2.3 Convergence of distributions 2.4 Central limit theoreras 2.5 Further ...

karaki, an outstanding faqih in 10th century (ah), was the first to cooperate with the safavids, hence founding the basis for the convergence of the ulama and the state in the safavid era. his theoretical contribution lies on the proposal of the theory of the sovereignty of faqih. with karaki being scientifically and politically famous, his theory soon became wide-spread in this period and was ...

In this paper, an -convergence theory of filters in an L -space is established. By means of the -convergence theory, some important characterizations with respective to the closed sets, T2 separation and (

In this paper, the theory of γ -convergence and γ c -convergence on nets and filters is established in fuzzifying topology. Some important and interesting results in fuzzifying topology are obtained by means of the theory.

the use of micro-controllers in actuators provides extended flexibility for on-line data acquisition and sophisticated control implementation. however, attempts to utilize the excellent features of induction motor that is deemed by its strength, robustness, high torque, and relatively low cost in actuators face a fundamental control design challenge. the purpose of this paper is to introduce th...