An event-triggered mechanism to observer-based sliding mode control of fractional-order uncertain switched systems.

This paper is dealing with the problem of observer-based event-triggered sliding mode control for fractional-order uncertain switched systems with a positive order less than one. Firstly, a fractional-order state observer is designed, based on which a fractional-order integral sliding surface function is proposed. Then, utilizing the estimated observer error and sliding mode error vectors, an event-triggered condition is constructed to decide whether the current control signal should be updated or not. Besides, sufficient conditions are derived in the forms of linear matrix inequalities (LMIs) to ensure finite-time stability of the augmented closed-loop system by adopting an average dwell time approach. Thereafter, to avoid the occurrence of infinite triggers within finite time, this paper also discusses the Zeno behavior and refines the results in the previous literature. Finally, to illustrate the effectiveness and superiority of the proposed method, three numerical simulations are provided.

Event-triggered observer-based H∞ sliding mode control of nonlinear systems.

The problem of sliding mode control for a class of Takagi-Sugeno fuzzy model-based nonlinear one-sided Lipschitz systems is investigated in the paper. Due to the state components are not available, a state observer is designed based on an event-triggering mechanism. Meanwhile, the output measurements transmitted through the communication channels suffer from signal delays. Based on the estimated state, an integral sliding surface is proposed. Then, the sliding mode dynamics is obtained by virtue of equivalent control principle. Further, by constructing appropriate sliding mode controller, the finite-time reachability of predefined sliding surface is surely guaranteed. Moreover, the stability with an H∞ performance analysis of sliding mode dynamics is undertaken via Lyapunov function theory and the criteria are established in terms of LMI. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed method.

Observer-based H∞ control design for singular switching semi-Markovian jump systems with random sensor delays.

This paper studies the problem of H∞ control design for a class of singular switching semi-Markovian jump systems, in which the transition rates of jumping process are uncertain and the output measurements suffer from random sensor delays. Firstly, a Luenberger observer is designed to estimate the system state components, based on which an error dynamic is obtained. Then, stochastic stability analysis for the overall closed-loop system is given based on the upper and lower bounds of transition rates. Further, the state feedback controller gain matrices are given by solving a set of sufficient conditions in terms of strict linear matrix inequalities (LMIs), which also guarantee the closed-loop system to be stochastically stabilizable and has a prescribed H∞ performance index γ. Finally, a numerical example is provided to verify the effectiveness of the obtained result.

Adaptive Control of Nonlinear Semi-Markovian Jump T-S Fuzzy Systems With Immeasurable Premise Variables via Sliding Mode Observer.

The issue of observer-based adaptive sliding mode control of nonlinear Takagi-Sugeno fuzzy systems with semi-Markov switching and immeasurable premise variables is investigated. More general nonlinear systems are described in the model since the selections of premise variables are the states of the system. First, a novel integral sliding surface function is proposed on the observer space, then the sliding mode dynamics and error dynamics are obtained in accordance with estimated premise variables. Second, sufficient conditions for stochastic stability with an H∞ performance disturbance attenuation level γ of the sliding mode dynamics with different input matrices are obtained based on generally uncertain transition rates. Third, an observer-based adaptive controller is synthesized to ensure the finite time reachability of a predefined sliding surface. Finally, the single-link robot arm model is provided to verify the control scheme numerically.

H∞ sliding mode control of discrete switched systems with time-varying delays.

The finite-time boundedness issue for a class of discrete switched systems with time-varying delays is investigated via sliding mode control (SMC) approach. By employing the Lyapunov functional and average dwell time method, new sufficient conditions are derived to guarantee the finite-time boundedness of the dynamic system in the novel sliding surface. By solving an optimization problem, the sliding mode controller is synthesized such that the discrete reaching condition is satisfied and the chattering is reduced. A simulation example tests the feasibility of the provided SMC scheme.

Robust observer-based H∞ control for uncertain discrete singular systems with time-varying delays via sliding mode approach.

In this paper, the issue of robust observer-based H∞ control for uncertain discrete singular systems with time-varying delays is investigated via sliding mode control (SMC). A sliding mode strategy is presented combined with the observer technique, since the system states are unmeasured. The distinguishing feature of the provided strategy is that a novel sliding surface is constructed based upon the estimated states such that the resulting full-order closed-loop system is generated. Furthermore, by employing Lyapunov-Krasovskii functional, new sufficient criteria in terms of a solvable linear matrix inequality (LMI) is derived, insuring that the closed-loop system is admissible with an H∞-norm bound. With the solution of the LMI, a corresponding sliding mode controller is obtained for reaching motion and reducing the chattering. At last, the theoretical results are verified in numerical tests.

Robust passive control for a class of uncertain neutral systems based on sliding mode observer.

The passivity-based sliding mode control (SMC) problem for a class of uncertain neutral systems with unmeasured states is investigated. Firstly, a particular non-fragile state observer is designed to generate the estimations of the system states, based upon which a novel integral-type sliding surface function is established for the control process. Secondly, a new sufficient condition for robust asymptotic stability and passivity of the resultant sliding mode dynamics (SMDs) is obtained in terms of linear matrix inequalities (LMIs). Thirdly, the finite-time reachability of the predesigned sliding surface is ensured by resorting to a novel adaptive SMC law. Finally, the validity and superiority of the scheme are justified via several examples.