This paper investigates the problems of two-dimensional (2-D) dissipative control and filtering for a linear discrete-time Roesser model. First, a novel sufficient condition is proposed such that the discrete-time Roesser system is asymptotically stable and 2-D $(Q,S,R)\hbox{-} \alpha$ -dissipative. Special cases, such as 2-D passivity performance and 2-D $H_{\infty} $ performance, and feedback interconnected systems are also discussed. Based on this condition, new 2-D $(Q,S,R)\hbox{-} \alpha$ -dissipative state-feedback and output-feedback control problems are defined and solved for a discrete-time Roesser model. The design problems of 2-D $(Q,S,R)\hbox{-} \alpha$ -dissipative filters of observer form and general form are also considered using a linear matrix inequality (LMI) approach. Two examples are given to illustrate the effectiveness and potential of the proposed design techniques.

Two-Dimensional Dissipative Control and Filtering for Roesser Model

Load frequency control (LFC) is a very important method to keep the power systems stable and secure. However, due to the introduction of communication networks in multi-area power systems, the traditional LFC method is not effective again. This motivates us to investigate an adaptive event-triggering ${H}_{\infty }$ LFC scheme for multi-area power systems. Compared with the existing time-invariant event-triggering communication scheme, an adaptive event-triggering communication scheme is presented, where the event-triggering threshold can be dynamically adjusted to save more limited network resources, while preserving the desired control performance. Compared with the existing emulation-based method, where the controller must be known a priori , the stability and stabilization criteria derived in this work can provide a tradeoff to balance the required communication resources and the desired control performance. The effectiveness of the proposed method is verified by two numerical examples.

Adaptive Event-Triggering ${H}_{\infty }$ Load Frequency Control for Network-Based Power Systems

Brief On the design of multivariable PID controllers via LMI approach

In this note, non-smooth finite-time stabilization of nonlinear systems with parametric and dynamic uncertainties is investigated. To solve this problem, the input-to-state stability property is used to characterize unmeasured dynamic uncertainties. A constructive partial-state control design is proposed on the basis of involved combined use of Lyapunov, backstepping and input-to-state stability techniques. Under small-gain type local conditions, a solution for the finite-time regulation of a class of uncertain nonlinear systems is obtained

Finite-Time Stabilization of Nonlinear Systems With Parametric and Dynamic Uncertainties

In this paper, we investigate the problem of robust static output feedback (SOF) control for networked control systems (NCSs) subject to network-induced delays and missing data. The uncertain system matrices are assumed to lie in a convex polytope. The network-induced delays are time varying but within a given interval. The random data missing is characterized by the Bernoulli random binary distribution. Delay-dependent conditions for the exponential mean-square stability are first established in terms of matrix inequalities. Then, for the robust stabilization problem, the design of an SOF controller is presented by solving bilinear matrix inequalities (BMIs). In order to efficiently solve a nonconvex BMI, we propose an approach based on the linear matrix inequality technique. Furthermore, the developed approach is employed to design the remote proportional-integral-derivative (PID) controller for NCSs. The design of a digital PID controller is formulated as a synthesis problem of the SOF control via an augmentation method. Simulation examples illustrate the effectiveness of the proposed methods.

Robust Static Output Feedback Control and Remote PID Design for Networked Motor Systems

The authors present linear matrix inequality (LMI) conditions for output feedback control problems. The results are based on sufficient conditions because they are dependent on the particular state-space representation used for describing the system. Nevertheless, the conditions are not sensitive to a certain class of state-space transformations, and if the control problem is feasible then there exists some state-space transformation leading the conditions to be necessary and sufficient for the problem. The authors approach can be used for designing decentralized controllers and is easily extended to H/sub 2/, H/sub /spl infin// and mixed H/sub 2//H/sub /spl infin// problems via standard LMI techniques. The continuous- and discrete-time cases are considered and numerical examples are given to illustrate the results.

C.A.R. Crusius

Papers

Sufficient LMI conditions for output feedback control problems