Lakshmanan Shanmugam

Improved delay-dependent stability criteria for neutral systems with mixed interval time-varying delays and nonlinear disturbances

It is well-known that the stability analysis of time-delay systems is a key step to design appropriate controllers and/or filters for those systems. In this paper, the problem of the delay-dependent stability analysis of neutral systems with mixed interval time-varying delays with/without nonlinear perturbations is revisited. Bounded derivatives of the discrete and neutral delays with upper-bounds not limited to be strictly less than one are considered. New stability criteria are developed using the Lyapunov Krasovskii methodology which are expressed in terms of linear matrix inequalities (LMIs). An augmented Lyapunov Krasovskii functional (LKF) utilizing triple integral terms and the descriptor transformation is employed to this aim. In addition, advanced techniques such as Wirtinger-based single and double-integral inequalities, delay decomposition technique combined with the reciprocally convex approach, as well as a few effective free-weighting matrices are employed to achieve less conservative stability conditions. Comprehensive benchmarking numerical examples and simulation studies demonstrate the effectiveness of the proposed stability criteria with respect to some recently published results. The efficacy of the modern integral inequalities are also emphasized against the conventional Jensen׳s inequalities.

Improved delay-dependent stability criteria for telerobotic systems with time-varying delays

This paper addresses the synchronization problem of telerobotic systems, in which the master and slave robots are assumed to be serial manipulators and the communication-delays are assumed to be time-varying and nonsymmetric with known lower and upper bounds. Proportional derivative, proportional, and position-force control structures are considered for passive and nonpassive human operator. Using the Lyapunov-Krasovskii methodology, delay-dependent stability conditions of the closed-loop system are established in the form of linear matrix inequalities. The stability criteria derived in this paper is shown to be less conservative than some of the existing results within the literature, and they amend the calculation of the control parameters and ensure the stability and transparency of the system for larger bounds of communication-delays. Simulation studies are performed to demonstrate the effectiveness of the proposed stability criteria in obtaining a larger stability region for the system.

Functional observer design for retarded system with interval time-varying delays

ABSTRACT Functional observers are the key solution to numerous practical estimation problems, wherein full-order observers cannot be applied. This paper studies the novel problem of minimum-order functional observer design for time-delay systems with interval time-varying state delays. Moreover, unlike the majority of the existing papers on this topic, which consider either small or unknown delay rates, the delay derivative is assumed to possess an upper bound not limited to be less than one. A new augmented Lyapunov–Krasovskii functional with triple integral terms is employed to derive less conservative delay-dependent sufficient conditions for the stability of the closed-loop observer dynamics, which are expressed in terms of linear matrix inequalities. In addition, contemporary techniques such as Wirtinger-based single- and double-integral inequalities, delay splitting scheme, reciprocally convex approach and convex combination technique, along with the descriptor transformation, are adopted in constructing the new stability criterion that is exploited for obtaining the observer parameters. A genetic-algorithm-based searching schema is proposed to optimally tune a number of weighting parameters in the observer design procedure. Numerical examples and simulation results are demonstrated to confirm the effectiveness and the superiority of the proposed observer design algorithm.

Partial state estimation of LTI systems with multiple constant time-delays

Abstract Functional observer design for Multi-Input Multi-Output (MIMO) Linear Time-Invariant (LTI) systems with multiple mixed time delays in the states of the system is addressed. Two structures for the design of a minimum-order observer are considered: 1 – delay-dependent , and 2 – internal-delay independent . The parameters of the delay-dependent observer are designed using the Lyapunov Krasovskii approach. The delay-dependent exponential stability of the observer for a specified convergence rate and delay values is guaranteed upon the feasibility of a set of Linear Matrix Inequalities (LMIs) together with a rank condition. Using the descriptor transformation, a modified Jensen׳s inequality, and improved Park׳s inequality, the results can be less conservative than the available functional observer design methods that address LTI systems with single state delay. Furthermore, the necessary and sufficient conditions of the asymptotic stability of the internal-delay independent observer are obtained, which are shown to be independent of delay. Two illustrative numerical examples and simulation studies confirm the validity and highlight the performance of the proposed theoretical achievements.

Robust H∞ cost guaranteed integral sliding mode control for the synchronization problem of nonlinear tele-operation system with variable time-delay

This paper is devoted to the synchronization problem of tele-operation systems with time-varying delay, disturbances, and uncertainty. Delay-dependent sufficient conditions for the existence of integral sliding surfaces are given in the form of Linear Matrix Inequalities (LMIs). This guarantees the global stability of the tele-operation system with known upper bounds of the time-varying delays. Unlike previous work, in this paper, the controller gains are designed but not chosen, which increases the degree of freedom of the design. Moreover, Wirtinger based integral inequality and reciprocally convex combination techniques used in the constructed Lypunove-Krasoviskii Functional (LKF) are deemed to give less conservative stability condition for the system. Furthermore, to relax the analysis from any assumptions regarding the dynamics of the environment and human operator forces, H∞ design method is used to involve the dynamics of these forces and ensure the stability of the system against these admissible forces in the H∞ sense. This design scheme combines the strong robustness of the sliding mode control with the H∞ design method for tele-operation systems which is coupled using state feedback controllers and inherit variable time-delays in their communication channels. Simulation examples are given to show the effectiveness of the proposed method.

A genetic algorithm–based nonlinear scaling method for optimal motion cueing algorithm in driving simulator

A motion cueing algorithm plays an important role in generating motion cues in driving simulators. The motion cueing algorithm is used to transform the linear acceleration and angular velocity of a vehicle into the translational and rotational motions of a simulator within its physical limitation through washout filters. Indeed, scaling and limiting should be used along within the washout filter to decrease the amplitude of the translational and rotational motion signals uniformly across all frequencies through the motion cueing algorithm. This is to decrease the effects of the workspace limitations in the simulator motion reproduction and improve the realism of movement sensation. A nonlinear scaling method based on the genetic algorithm for the motion cueing algorithm is developed in this study. The aim is to accurately produce motions with a high degree of fidelity and use the platform more efficiently without violating its physical limitations. To successfully achieve this aim, a third-order polynomial scaling method based on the genetic algorithm is formulated, tuned, and implemented for the linear quadratic regulator–based optimal motion cueing algorithm. A number of factors, which include the sensation error between the real and simulator drivers, the simulator’s physical limitations, and the sensation signal shape-following criteria, are considered in optimizing the proposed nonlinear scaling method. The results show that the proposed method not only is able to overcome problems pertaining to selecting nonlinear scaling parameters based on trial-and-error and inefficient usage of the platform workspace, but also to reduce the sensation error between the simulator and real drivers, while satisfying the constraints imposed by the platform boundaries.

H ∞ based state feedback robust controller for nonlinear tele-operation system with variable time-delays

This paper is devoted to the problem of robust control for a nonlinear tele-operation system with variable time-delay. Proportional (P) control scheme is used to couple the master and slave robotic arms bilaterally. Lyapunov-Krasovskii Functional (LKF) and H∞ design method is used to develop delay-dependent stability conditions that are robust to the variations of the exogenous inputs from the operator and environment in the form of Linear Matrix Inequality (LMI). The stability conditions are solved using Matlab LMI toolbox to obtain the values of the control parameters and the upper bounds of the variable time-delays in the forward and backward communication channels. The designed controller efficiency is demonstrated using simulations.

Synchronization Criteria for Delay Coupled Izhikevich Neurons

In this chapter, we investigate the chaotic synchronization of two coupled Izhikevich neurons via a gap junction. In the absence of a controller, the coupled neurons will achieve complete chaotic synchronization only when the degree of connectivity or the coupling strength exceeds a critical value. This transition to synchronization with varying connectivity strengths is analysed with conditional Lyapunov exponents. Synchronization of gap junction separated, coupled Izhikevich neurons using control laws has remained non-investigated to this date. As such, in this chapter we propose a nonlinear adaptive controller, in order to obtain complete chaotic synchronization for any value of coupling strength and delay, based on the Lyapunov stability theory. Effectiveness of the proposed nonlinear controller for synchronizing delayed-coupled Izhikevich neurons are shown through numerical simulations.