Finite-time stability and stabilization for stochastic markov jump systems with mode-dependent time delays

This paper is concerned with the problems of finite-time stability and stabilization for stochastic Markov systems with mode-dependent time-delays. In order to reduce conservatism, a mode-dependent approach is utilized. Based on the derived stability conditions, state-feedback controller and observer-based controller are designed, respectively. A new N-mode algorithm is given to obtain the maximum value of time-delay. Finally, an example is used to show the merit of the proposed results.     

Adaptive exponential stabilization for a class of nonlinear retarded processes

This paper considers the problem of adaptive exponential stabilization for a class of single-input single-output nonlinear retarded processes. The class includes certain linear retarded systems which are subject to sector-bounded actuator and sensor nonlinearities. It is shown that there is a wide range of high-gain adaptive compensators which achieve exponential stability for the class of processes under consideration. This work was supported by SERC under Grant No. GR/D/45710.     

Stochastic averaging analysis of a steepest-descent-type adaptive time-delay estimation algorithm

In this paper stochastic averaging analysis tools are used to study an adaptive time-delay estimation algorithm. Analyzing such an algorithm is very difficult because of its nonlinear, infinite-dimensional, and time-variant nature. By stochastic averaging analysis, we show that for the time-invariant delay case, the adaptive algorithm output converges weakly to the solution of an ordinary differential equation. Local convergence is demonstrated by showing that the solution of this differential equation converges exponentially to the true delay under reasonable initial conditions. Implementation of the algorithm is also discussed. Guided by the averaging results, a modified algorithm is proposed to eliminate the bias of the delay estimation. Second-order analysis is carried out and the results provide a theoretical justification of the observations made by other researchers with simulation and heuristic argument. Computer simulations are also included to support the analysis.     

Identification of time delays using a polynomial identification method

An algorithm for the exact least-squares identification of an approximate continuous-time time-delay system is derived and its operation verified by simulation.     

Proportional-delayed controllers design for LTI-systems: a geometric approach

This paper focuses on the design of P-δ controllers for single-input-single-output linear time-invariant systems. The basis of this work is a geometric approach allowing to partitioning the parameter space in regions with constant number of unstable roots. This methodology defines the hyper-planes separating the aforementioned regions and characterises the way in which the number of unstable roots changes when crossing such a hyper-plane. The main contribution of the paper is that it provides an explicit tool to find P-δ gains ensuring the stability of the closed-loop system. In addition, the proposed methodology allows to design a non-fragile controller with a desired exponential decay rate σ. Several numerical examples illustrate the results and a haptic experimental set-up shows the effectiveness of P-δ controllers.     

Discretization of nonlinear systems with delayed multi-input via Taylor series and scaling and squaring technique

An input time delay always exists in practical systems. Analysis of the delay phenomenon in a continuous-time domain is sophisticated. It is appropriate to obtain its corresponding discrete-time model for implementation via digital computers. In this paper a new scheme for the discretization of nonlinear systems using Taylor series expansion and the zero-order hold assumption is proposed. The mathematical structure of the new discretization method is analyzed. On the basis of this structure the sampled-data representation of nonlinear systems with time-delayed multi-input is presented. The delayed multi-input general equation has been derived. In particular, the effect of the time-discretization method on key properties of nonlinear control systems, such as equilibrium properties and asymptotic stability, is examined. Additionally, hybrid discretization schemes that result from a combination of the scaling and squaring technique (SST) with the Taylor series expansion are also proposed, especially under conditions of very low sampling rates. Practical issues associated with the selection of the method’s parameters to meet CPU time and accuracy requirements, are examined as well. A performance of the proposed method is evaluated using a nonlinear system with time delay: maneuvering an automobile.     

Adaptive super-twisting fractional-order nonsingular terminal sliding mode control of cable-driven manipulators

This paper proposes a novel adaptive super-twisting fractional-order nonsingular terminal sliding mode (AST–FONTSM) control scheme using time delay estimation (TDE) for the cable-driven manipulators. The designed control scheme utilizes TDE to obtain the estimation of system dynamics, and therefore no system dynamic model information will be required. Afterwards, AST and FONTSM schemes are applied to ensure good control performance in both reaching and sliding mode phases. Due to the adoption of AST scheme, good robustness and high control precision are obtained in the reaching phase, while the boundary information of the lumped uncertainties will be no longer required. Thanks to the utilization of FONTSM error dynamics, fast convergence and accurate tracking and strong robustness can be simultaneously ensured in the sliding mode phase. Corresponding comparative simulation and experimental results demonstrate the effectiveness and superiorities of our proposed method over the existing control methods.     

Feedback linearization via state transformation using estimated states

This paper deals with the exact feedback linearization of nonlinear plants using estimated states. Under appropriate hypotheses, exact linearization can be achieved through transformation of states and feedback. We assume that the states cannot be measured so that a nonlinear observer, with exponential convergence, is included in the loop. We establish sufficient conditions to guarantee that the overall system trajectories asymptotically converge to those obtained with feedback linearization utilizing the true states. We apply our results to control an electrical drive using a permanent-magnet synchronous motor without mechanical and optical sensors. The behaviour of our control scheme is illustrated by simulations.     

System identification with measurement noise compensation based on polynomial modulating function for fractional-order systems with a known time-delay

This study presents a system identification method based on polynomial modulating function for fractional-order systems with a known time-delay involving input and output noises in the time domain. Based on the polynomial modulating function and fractional-order integration by parts, the identified fractional-order differential equation is transformed into an algebraic equation. By using the numerical integral formula, the least squares form for the system identification is obtained. In order to reduce the effect of noises existing in the input and output measurements, the compensation method for the input and output noises is also studied by introducing an auxiliary high-order fractional-order system in the revised identification algorithm. Finally, the effectiveness of the proposed algorithm is verified by the simulation result of an illustrative example and the experimental result of temperature identification for a thermal system.     

Delay-dependent anti-windup synthesis for stability of constrained state delay systems using pole-constraints

This paper proposes the design of anti-windup compensator gain for stability of actuator input constrained state delay systems using constrained pole-position of the closed-loop. Based on Delay-Dependent Lyapunov-Krasovskii functionals and local sector conditions, a new LMI characterization is derived that ensures closed-loop asymptotic stability of constrained state delay systems while accounting upper bound fixed state delay and largest lower bound of the system’s pole-position in the formulation of anti-windup gain. Besides, at saturation, the method significantly nullifies the inherent slow dynamics present in the system. It is shown in the comparative numerical examples that the LMI formulation draws stability with improved time-domain performance.