Non-fragile dynamic output feedback control for linear systems with time-varying delay

This paper is concerned with analyzing a novel model transformation of discrete-time Takagi-Sugeno (T-S) fuzzy systems with time-varying delays and applying it to dynamic output feedback (DOF) controller design. A new auxiliary model is proposed by employing a new approximation for time-varying delay state, and then delay partitioning method is used to analyze the scaled small gain of this auxiliary model. A sufficient condition on discrete-time T-S fuzzy systems with time-varying delays, which guarantees the corresponding closed-loop system to be asymptotically stable and has an induced l 2 disturbance attenuation performance, is derived by employing the scaled small gain theorem. Then the solvability condition for the induced l 2 DOF control is also established, by which the DOF controller can be found by solving a set of linear matrix inequalities (LMIs).

In this paper, the $\boldsymbol{L}_{\infty}$ control synthesis problem for linear systems subject to actuator saturation and persistent bounded disturbance is studied. An $\boldsymbol{L}_{\infty}$ dynamic output feedback controller, an anti-windup compensator and an event generator are simultaneously designed. First, by using the quadratic Lyapunov function technique, a sufficient condition on the existence of the $\boldsymbol{L}_{\infty}$ dynamic output feedback controller, an anti-windup compensator and an event generator is established via linear matrix inequalities (LMIs). Such an integrated controller is able to guarantee the regional stabilization and the $\boldsymbol{L}_{\infty}$ performance of linear systems with actuator saturation and external persistent bounded disturbance. Second, novel algorithms are developed to optimize the upper bound on the $\boldsymbol{L}_{\infty}$ performance, the event-triggered threshold and the domain of attraction. Moreover, an output-based event-triggered mechanism applying to the anti-windup dynamic output feedback control design is provided, which reduces the number of control actuation updates and information transmission with respect to the traditional time-triggered control scheme.

In this paper, we study stability analysis and stabilization problems for a class of nonlinear two-dimensional (2-D) discrete systems with time-varying state delays, described by local state-space (LSS) Fornasini-Marchesini (FM) second model. The upper and lower bounds of time-varying state delays are positive integers and the nonlinearity satisfies Lipschitz condition. First, a stability criteria is proposed through introducing a new Lyapunov function. Then a dynamic output feedback controller is designed to assure the stability of nonlinear 2-D time-varying systems. Moreover, the output feedback system matrices can be obtained by solving linear matrix inequalities (LMIs). Finally, a numerical example is given to demonstrate the effectiveness of our results.

In this paper, the problem of L 2 -L ∞ dynamic output feedback controller design for the nonlinear switched system in the T-S fuzzy framework is investigated. First, the average dwell time approach is used to stabilize the nonlinear switched systems under an arbitrary switching law. Then, based on the piecewise Lyapunov function, the fuzzy-rule-dependent dynamic output feedback controller is designed to ensure that the overall closed-loop system is exponentially stable with a weighted :L 2 -L ∞ performance. Finally, the solvability condition of the desired output feedback controller is obtained by the linearization procedure technique, which can be calculated by available software.

In this paper, the event-triggered dynamic output feedback controller design problem is addressed for a class of discrete-time nonlinear systems in network environment. An augmented closed-loop system is constructed and the sufficient conditions to ensure the mean-square asymptotically stability of the closed-loop system with a Hankel-norm performance by considering the event-triggered condition and using the reciprocally convex technique. It is shown that the solution of the fuzzyrule-dependent dynamic output feedback controller parameters can be obtained by variable substitution method. An example is provided to demonstrate the effectiveness of the proposed design method.

Dynamic output feedback controller design for affine T–S fuzzy systems with quantized measurements

Dynamic output-feedback-based [formula omitted] design for networked control systems with multipath packet dropouts

This paper considers the design problems of a delay-dependent robust and non-fragile guaranteed cost controller for singular systems with parameter uncertainties and time-varying delays in state and control input. The designed controller, under the possibility of feedback gain variations, can guarantee that a closed-loop system is regular, impulse-free, stable, an upper bound of guaranteed cost function, and non-fragility in spite of parameter uncertainties, time-varying delays, and controller fragility. The existence condition of the controller, the controller’s design method, the upper bound of guaranteed cost function, and the measure of non-fragility in the controller are proposed using the linear matrix inequality (LMI) technique. Finally, numerical examples are given to illustrate the effectiveness and less conservatism of the proposed design method.

This paper establishes a framework for stability analysis and memoryless state-feedback control synthesis of linear discrete-time systems with time varying state delay. The underlying idea is converting the considered system into an equivalent constrained switched system, leading to sufficient and necessary condition for stability analysis. Based on this switched system modeling, available information about the time-varying delay such as known bounds of variation rate can be incorporated into the analysis in a natural way. Moreover, sufficient conditions for memoryless state-feedback control design are obtained in a similar style. The analysis and synthesis conditions are given in terms of solvability of a set of linear matrix inequalities (LMIs). Numerical examples are included for illustration.

The robust passivity synthesis problem is addressed for a class of uncertain delayed systems with time-varying delays in both state and control input. The parameter uncertainties are norm-bounded and allowed to appear in all the matrices of the model. The problem aims at designing an observer-based dynamic controller that renders the closed-loop systems strongly robustly stable with strictly passive for all admissible uncertainties, dependently of the maximum of delay derivative. By converting the problem at present into a class of strongly stable with strictly passive control problem for some parameterized systems equivalently, the explicit solution is established and expressed in terms of a linear matrix inequality.

This paper is concerned with the problem of delay-derivative-dependent stability analysis for Markovian jumping neutral-type interval time-varying delay systems with mixed delays. The first, based on the Lyapunov-Krasovskii stability theory for functional differential equations and the linear matrix inequality approach, a delay-range-dependent condition for neutral-type Markovian jumping systems (NMJSs) with time-varying delays is obtained, which can guarantee global asymptotical stability of these NMJSs. Unlike the previous methods, the upper bound of the discrete delay and neutral delay derivative is taken into consideration even if this upper bound is larger than or equal to $$1(\dot{h}(t)<1,\dot{\tau}(t)<1)$$ . It is proved that the obtained results are less conservative than the existing ones. In our result, the time-varying delays are only assumed to be bounded. This has undoubtedly extended its application range. To better handle the problem on stability for neutral control systems, in which time-varying delay was involved, a stability criterion with less conservatism was put forward. Moreover, because our results in this paper are all based on the linear matrix inequality (LMI) approach, we can utilize Matlab’s LMI Control Toolbox to verify the global stability of correlation systems conveniently. As far as we are aware, this paper seems to be the first to discuss stability problems for neutral-type Markovian jumping systems with delay-derivative-dependence and delay-range-dependence.

For quasi-linear parameter varying (quasi-LPV) systems with bounded disturbance, a synthesis approach of dynamic output feedback robust model predictive control (OFRMPC) with the consideration of input saturation is investigated. The saturated dynamic output feedback controller is represented by a convex hull involving the actual dynamic output controller and an introduced auxiliary controller. By taking both the actual output feedback controller and the auxiliary controller with a parameter-dependent form, the main optimization problem can be formulated as convex optimization. The consideration of input saturation in the main optimization problem reduces the conservatism of dynamic output feedback controller design. The estimation error set and bounded disturbance are represented by zonotopes and refreshed by zonotopic set-membership estimation. Compared with the previous results, the proposed algorithm can not only guarantee the recursive feasibility of the optimization problem, but also improve the control performance at the cost of higher computational burden. A nonlinear continuous stirred tank reactor (CSTR) example is given to illustrate the effectiveness of the approach.

This paper studies the problem of linear matrix inequality (LMI) approach to robust stability analysis for stochastic neural networks with a time-varying delay. By developing a delay decomposition approach, the information of the delayed plant states can be taken into full consideration. Based on the new Lyapunov—Krasovskii functional, some inequality techniques and stochastic stability theory, new delay-dependent stability criteria are obtained in terms of LMIs. The proposed results prove the less conservatism, which are realized by choosing new Lyapunov matrices in the decomposed integral intervals. Finally, numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI method.

In this article, the adaptive consensus tracking control is developed for uncertain multiagent systems with time-varying state delay in the case that leader's state is accessible at sampling instants. By proposing a distributed sampled observer with hybrid form, adaptive tracking controller with the complementary term is designed for first-order multiagent systems, and then is extended to high-order multiagent systems with the aid of dynamic surface control. Through the complementary term, the effects of parameter estimation error as well as dynamical terms with time-varying delays are eliminated and thus less conservative condition on time delays is required. It is proved that, under criteria in terms of linear matrix inequalities (LMIs), tracking error and estimation error exponentially converge to zero for first-order systems, and to a sufficiently small neighborhood of zero for high-order systems.

This paper addresses the stability analysis and dynamic output feedback control for a class of T–S fuzzy networked control systems with mixed time-varying delays and interval distributed time-varying delays. Firstly, the T–S fuzzy model is employed to approximate the networked control system based on the system model. Secondly, the dynamic output feedback controller with hybrid intermittent feedback control law is designed for the T–S fuzzy networked control system. Thirdly, the delay-dependent stability conditions are derived by introducing the Lyapunov functional with Leibniz–Newton formula. Compared with previous works, both the mixed time-varying delays and interval distributed time-varying delays are considered in the T–S fuzzy networked control system. The control design conditions are relaxed because of the proposed controller. By introducing the Lyapunov functional with Leibniz–Newton formula, the linear matrix inequalities are solved effectively by the standard convex optimization algorithm. Finally, the simulation examples and some computing results are given to show the effectiveness and advantage of the proposed method, respectively.