Bounded real lemma and robust control of 2-D singular Roesser models

This paper discusses the problem of robust H_∞ control for linear discrete time two-dimensional (2-D) singular Roesser models (2-D SRM) with time-invariant norm-bounded parameter uncertainties. The purpose is the design of static output feedback controllers such that the resulting closed-loop system is acceptable, jump modes free, stable and satisfies a prescribed H_∞ performance level for all admissible uncertainties. A version of bounded realness of 2-D SRM is established in terms of linear matrix inequalities. Based on this, a sufficient condition for the solvability of the robust H_∞ control problem is solved, and a desired output feedback controller can be constructed by solving a set of matrix inequalities. A numerical example is provided to demonstrate the applicability of the proposed approach.     

Improved delay-dependent stability criteria for time-delay systems

This note provides an improved asymptotic stability condition for time-delay systems in terms of a strict linear matrix inequality. Unlike previous methods, the mathematical development avoids bounding certain cross terms which often leads to conservatism. When time-varying norm-bounded uncertainties appear in a delay system, an improved robust delay-dependent stability condition is also given. Examples are provided to demonstrate the reduced conservatism of the proposed conditions.     

Improved global robust asymptotic stability criteria for delayed cellular neural networks.

This paper considers the problem of global robust stability analysis of delayed cellular neural networks (DCNNs) with norm-bounded parameter uncertainties. In terms of a linear matrix inequality, a new sufficient condition ensuring a nominal DCNN to have a unique equilibrium point which is globally asymptotically stable is proposed. This condition is shown to be a generalization and improvement over some previous criteria. Based on the stability result, a robust stability condition is developed, which contains an existing robust stability result as a special case. An example is provided to demonstrate the reduced conservativeness of the proposed results.     

STOCHASTIC STABILIZATION AND H∞ CONTROL FOR DISCRETE JUMPING SYSTEMS WITH TIME DELAYS

In this paper, robust stochastic stabilization and H_∞ control for a class of uncertain discrete‐time linear systems with Markovian jumping parameters are considered. Based on a new bounded real lemma derived upon an inequality recently proposed, a new iterative state‐feedback controller design procedure for discrete time‐delay systems is presented. Sufficient conditions for stochastic stabilization are derived in the form of linear matrix inequalities (LMIs) based on an equivalent model transformation, and the corresponding H_∞ control law is given. Finally, numerical examples are given to illustrate the solvability of the problems and effectiveness of the results.     

Exponential dynamic output feedback controller design for stochastic neutral systems with distributed delays

This paper investigates the problem of stochastic stabilization for stochastic neutral systems with distributed delays. The time delay is assumed to appear in both the state and measurement equations. Attention is focused on the design of linear dynamic output feedback controllers such that the resulting closed-loop system is exponentially mean-square stable. A sufficient condition for the solvability of the problem is obtained in terms of a linear matrix inequality (LMI). When this LMI is feasible, an explicit expression of a desired dynamic output feedback controller is also given. The theory developed in this paper is demonstrated via a numerical example.     

Solving Inheritance Anomaly with OMNets

This paper presents a concurrent object-oriented modeling language based on Petri nets:OMNets,which hepls greatly to avoid the inheritance anomaly problem appeared in concurrent OO languages.OMNets separates th functional part and the synchroniztion part of objects and uses Petri nets to describe the synchronization part.Both parts are reusable through inheritance.     

On H<Subscript>∞</Subscript> Filtering for a Class of Uncertain Nonlinear Neutral Systems

This paper investigates the problem of robust H filtering for a class of nonlinear neutral systems with norm-bounded parameter uncertainties appearing in all the matrices of the linear part of the system model. The nonlinearities are assumed to satisfy the global Lipschitz conditions and appear in both the state and measured output equations. The problem we address is the design of a nonlinear filter that guarantees both the robust stability and a prescribed H performance of the filtering error dynamics irrespective of the parameter uncertainties. A sufficient condition for the solvability of this problem is given in terms of a linear matrix inequality (LMI). When this LMI is feasible, the expression of a desired H filter is also presented. A numerical example is provided to demonstrate the effectiveness of the proposed approach.     

An algebraic approach to the robust stability analysis and robust stabilization of uncertain singular systems

This paper considers the problems of robust stability analysis and robust stabilization for uncertain singular systems with norm-bounded time-varying uncertainties. The robust stability problem is solved via the notion of generalized quadratic stability which guarantees that the uncertain singular system is stable, regular and impulse free simultaneously for all admissible uncertainties, while the robust stabilization problem is solved via the notion of generalized quadratic stabilizability. An algebraic approach is adopted in the paper. Our main results are extensions of some existing results on uncertain regular systems for singular systems.     

Positive real control of two-dimensional systems: Roesser models and linear repetitive processes

This paper considers the problem of positive real control for two-dimensional (2-D) discrete systems described by the Roesser model and also discrete linear repetitive processes, which are another distinct sub-class of 2-D linear systems of both systems theoretic and applications interest. The purpose of this paper is to design a dynamic output feedback controller such that the resulting closed-loop system is asymptotically stable and the closed-loop system transfer function from the disturbance to the controlled output is extended strictly positive real. We first establish a version of positive realness for 2-D discrete systems described by the Roesser state space model, then a sufficient condition for the existence of the desired output feedback controllers is obtained in terms of four LMIs. When these LMIs are feasible, an explicit parameterization of the desired output feedback controllers is given. We then apply a similar approach to discrete linear repetitive processes represented in their equivalent 1-D state-space form. Finally, we provide numerical examples to demonstrate the applicability of the approach.     

Robust H ∞ filtering for a class of non-linear systems with state delay and parameter uncertainty

This paper deals with the problem of robust H X filtering for a class of state-delayed non-linear systems with normbounded parameter uncertainty appearing in all the matrices of the linear part of the system model. The non-linearities are assumed to satisfy the global Lipschitz conditions and appear in both the state and measured output equations. Attention is focused on the design of a non-linear filter which ensures both the robust stability and a prescribed H X performance of the filtering error dynamics for all admissible uncertainties. A sufficient condition for the existence of such a filter is given in terms of a linear matrix inequality (LMI). When this LMI is feasible, the expression of a desired H X filter is also presented. A numerical example is provided to demonstrate the applicability of the proposed approach.