Yulian Jiang

Reliable observer-based H∞ control for discrete-time fuzzy systems with time-varying delays and stochastic actuator faults via scaled small gain theorem

Abstract This paper is concerned with the reliable observer-based H ∞ control problem for discrete-time Takagi–Sugeno (T–S) fuzzy systems with time-varying delay and stochastic actuator faults based on input–output approach. A discrete-time homogeneous Markov chain is used to represent the stochastic behavior of actuator faults. First, the discrete-time T–S fuzzy system is transformed into the form of interconnection of two subsystems by employing a new model transformation for the delayed state variables. Furthermore, a sufficient condition on discrete-time T–S fuzzy systems with time-varying delay and actuator faults, which guarantees the corresponding closed-loop system to be stochastically stable and preserves a guaranteed H ∞ performance, is derived by employing the scaled small gain theorem. Meanwhile, the solvability condition for the reliable observer-based H ∞ control is also established, by which the reliable H ∞ fuzzy controller can be solved as linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.

Fault detection and control co-design for discrete-time delayed fuzzy networked control systems subject to quantization and multiple packet dropouts

Abstract This paper investigates the problem of fault detection (FD) for discrete-time delayed fuzzy networked control systems with quantization and packet dropouts. Different from existing results for FD, the proposed ones are toward closed-loop design problem, that is, the controller gain, and the fault detection filter (FDF) gains are designed simultaneously. The missing phenomenon is assumed to occur, in the communication links for quantizer-to-FDF and controller-to-physical plant, where the missing probability of packet dropouts is governed by an individual random binary distribution, while the quantization errors are treated as sector-bound uncertainties. The discrete-time fuzzy networked system is first transformed into the form of interconnection of two subsystems by applying an input–output method and a two-term approximation approach, which is employed to approximate the time-varying delay. Our attention is focused on the design of fuzzy fault detection filter (FFDF) such that, for all data missing conditions, and measurement quantization, the residual system is stochastically stable with a guaranteed H ∞ performance. Sufficient conditions are first established via introducing some slack matrices to facilitate the FDF design procedure by eliminating the coupling between the Lyapunov matrices and the system matrices. Numerical examples are provided to demonstrate the effectiveness and applicability of the proposed method.

Event-triggered based distributed H∞ consensus filtering for discrete-time delayed systems over lossy sensor network

This paper investigates the issue of event-triggered distributed H∞ consensus filtering for discrete time-varying delay systems over lossy sensor networks with stochastic switching topologies. For each sensor node, the event-triggering mechanism is given by an event detector, which determines whether to transmit the output measurement or not. The communication links between the event detector and the distributed filter are assumed to be over a lossy network, and the missing probability is governed by a set of random variables. Through available output measurements from not only the individual sensor but also its neighbouring sensors, according to the interconnection topology to estimate the system states, a sufficient condition is established for the desired distributed filter to ensure that the overall filtering dynamics are stochastically stable and achieve a prescribed distributed H∞ average performance. Meanwhile, the corresponding solvability conditions for the desired distributed filter gains are characterized in terms of feasibility linear matrix inequalities. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed approaches.

Average dwell time approach to H∞ filter for continuous-time switched linear parameter varying systems with time-varying delay

Considering two types of delays including both time-varying delay and parameter varying delay in continuous switched linear parameter varying systems, the problem of H ∞ filtering under average dwell time switching is illustrated. The H ∞ filter depending on the linear time-varying parameter ρ ( t ) (mode-dependent parameterized filter) is designed at first. Then, based on multiple Lyapunov function and an improved reciprocally convex inequality, the corresponding existence sufficient conditions for the filter could ensure the obtained filter error system exponentially stable with a guaranteed H ∞ performance in the form of linear matrix inequalities. In addition, the designed filter gains under allowed switching signals are computed via the proposed convex optimal algorithm. In the end, two numerical examples show the effectiveness of the results in this work.

Distributed H∞ consensus control for nonlinear multi-agent systems under switching topologies via relative output feedback

For a class of nonlinear multi-agent systems under switching topologies with disturbances, we propose a distributed H∞ consensus control protocol based on relative output feedback and utilize an iterative algorithm for solving nonlinear matrix inequality in this paper. Firstly, a consensus control protocol via relative output feedback is designed. Then, an iterative algorithm is utilized to calculate nonlinear matrix inequality. By this, the output feedback gain is designed but not chosen, which increases the design degree of freedom and meanwhile H∞ performance index γ is obtained. Finally, the proposed theory is applied to multiple simple-pendulums network systems driven by DC motors, and simulation results show the effectiveness of the designed consensus control protocol.

Improvement of reliable H ∞ control for discrete-time fuzzy systems with time-varying delays

This paper is concerned with the reliable H∞ control problem for discrete-time Takagi-Sugeno (T-S) fuzzy systems with time-varying delays and stochastic actuator faults based on a novel summation inequality. A discrete-time homogeneous Markov chain is used to represent the stochastic behavior of actuator faults. By employing a fuzzy basis-dependent Lyapunov functional and the novel summation inequality, an improved sufficient condition is established to ensure that the resultant closed-loop system is stochastically stable with an H∞ performance index. Meanwhile, the solvability condition for the reliable H∞ control is also established, by which the reliable H∞ fuzzy controller can be solved from linear matrix inequalities. A numerical example is provided to demonstrate the effectiveness of the present approach.