A delay distribution based stability analysis and synthesis approach for networked control systems

Communication delays in networked control systems (NCSs) has been shown to have non-uniform distribution and multifractal nature. This paper proposes a delay distribution based stability analysis and synthesis approach for NCSs with non-uniform distribution characteristics of network communication delays. A stochastic control model related with the characteristics of communication networks is established to describe the NCSs. Then, delay distribution-dependent NCS stability criteria are derived in the form of linear matrix inequalities (LMIs). Also, the maximum allowable upper delay bound and controller feedback gain can be obtained simultaneously from the developed approach by solving a constrained convex optimization problem. Numerical examples showed that the results derived from the proposed method are less conservativeness than those derived from the existing methods.     

New robust delay-dependent stability and H∞ analysis for uncertain Markovian jump systems with time-varying delays

This paper deals with the problems of robust delay-dependent stability and H_∞ analysis for Markovian jump linear systems with norm-bounded parameter uncertainties and time-varying delays. In terms of linear matrix inequalities, an improved delay-range-dependent stability condition for Markovian jump systems is proposed by constructing a novel Lyapunov-Krasovskii functional with the idea of partitioning the time delay, and a sufficient condition is derived from the H_∞ performance. Numerical examples are provided to demonstrate efficiency and reduced conservatism of the results in this paper.     

H∞ guaranteed cost control for uncertain Markovian jump systems with mode-dependent distributed delays and input delays

This paper investigates the H_∞ guaranteed cost control problem for mode-dependent time-delay jump systems with norm-bounded uncertain parameters. Both distributed delays and input delays appear in the system model. Based on a matrix inequality, a sufficient condition for the existence of robust H_∞ guaranteed cost controller is derived, which stabilizes the considered system and guarantees that both the H_∞ performance level and a cost function have upper bounds for all admissible uncertainties. By the cone complementary linearization approach, the desired state-feedback controller can be constructed. A numerical example is provided to show the effectiveness of the proposed theoretical results.     

Delay-dependent stochastic stability and H∞ analysis for time-delay systems with Markovian jumping parameters

This paper studies the problem of the stochastic stability and H_∞ disturbance attenuation for linear continuous-time time-delay systems that possess randomly Markovian jumping parameters. A delay-dependent sufficient condition on the stochastic stability with given H_∞ performance is proposed using the stochastic Lyapunov–Krasovskii stability theory. The conditions are formulated as a set of coupled linear matrix inequalities.     

H∞ filtering for linear neutral systems with mixed time-varying delays and nonlinear perturbations

In this paper, the problem of H_∞ filtering for neutral systems with mixed time-varying delays and nonlinear perturbations is investigated. Some new delay-dependent sufficient conditions are presented to ensure that the filtering error system is asymptotically stable with a prescribed level of H_∞ noise attenuation. In addition, the design procedures for the existence of such filter are presented in terms of a set of linear matrix inequalities (LMIs). Slack variables and convex combination technique are adopted to reduce the conservatism of obtained results. Finally, three numerical examples are given to illustrate the effectiveness of the proposed method.