The paper deals with the problem of compensation of unmeasured output biased harmonic disturbance for nonlinear plant. We propose a frequency identifier for unmeasured biased harmonic disturbance. Using this identifier the disturbance compensation algorithm was designed. This algorithm is based on observing the extended plant model and designing a control signal for the disturbance compensation by measured states of the designed observer. It is demonstrated that the proposed algorithm is applicable under variable disturbance frequency.

 In this paper we provide an algorithm for nonlinear regular proper DAEs to derive a controller for an associated state space system assuming the algebraic variables and the error of the algebraic equations as fictitious inputs and outputs, respectively. It is shown that the achieved controlled state space representation has the same solution as the original DAE in the case of consistent initial values. Therefore, it can be used for stability analysis, designing control laws, and the numerical integration with standard methods. In contrast to the realization in minimal coordinates this formulation can be derived straightforward and the computation is easy to implement on a computer algebra system.

 Modeling, control design and stability of series-connected dc motors fed by three-phase ac/dc voltage source converters are investigated. The design developed in this paper results in a twin nonlinear controller structure each acting as an oscillator with damped frequency and complementary tasks, i.e. to achieve precise motor speed regulation and operation with unity power factor. An extended passivity-based analysis shows that the proposed approach guarantees the system damping which is essential for stability analysis. To this end, by using the sequence of linear time-varying approximations method, it is proven that the system with the external unknown input is attracted to the desired equilibrium. Furthermore, it becomes clear that the proposed controller does not need any measurement or knowledge of the system conditions and parameters. Stability analysis and these properties constitute the main advantages of this control design approach with respect to other existing schemes. Simulation results verify the controller performance under speed reference and load torque changes.

 In this paper, we define Lagrange stability and input-to-state stability on manifolds.Furthermore, we present necessary and sufficient conditions for stability by using continuous positive definite proper functions.

 In this paper, we discuss almost sure asymptotic stability for deterministic systems, which are randomized by adding one-dimensional standard Wiener processes. First, we clarify the difference between the deterministic Lyapunov stability theory and the stochastic stability theory proposed by Hasminskii, and show that local asymptotic stability in probability causes trouble in randomization problems. Second, we describe the Lyapunov stability theory based on almost sure stability, as proposed by Bardi and Cesaroni, and show that the stability is ``almost the same'' as the deterministic Lyapunov stability. Third, we survey randomization problems briefly, and show that Stratonovich integrals are valid for such problems based on one-dimensional Wiener processes. Finally, we derive the necessary conditions for stochastic Lyapunov functions to ensure almost sure stabilities and discuss the difference between Hasminskii's stabilities and those of Bardi and Cesaroni via linear stochastic systems with numerical simulations.

 This paper presents a systematic approach to find a Lyapunov function for stability analysis of pseudo Euler-Lagrange systems. There are two main contributions of this paper. First, a systematic procedure is proposed to obtain a Lyapunov function for the system directly from the mathematical structure of the differential equations, without the need to determine any kinetic or potential energy of the system first. Second, energy-based ideas used in Euler-Lagrange systems are extended to the case where generalized velocity variables are not necessarily the derivative of generalized position variables. The method proposed here works for any mathematical model in the class of pseudo Euler-Lagrange systems and is therefore not restricted to models of physical systems, having thus the potential to address economic, biologic and other systems. Several examples illustrate the application of the new approach.