LMI approach to static output feedback simultaneous stabilization of discrete-time interval systems with time delay

This paper will research the problem of static output feedback (SOF) stabilization of state-constrained switched linear systems via an improved average dwell time method (ADT). Firstly, an improved ADT method is adopted to establish sufficient conditions for SOF of the state-constrained switched linear systems in the form of matrix inequality. It has been shown that this method is less conservative than traditional ADT, which in view of different decay rates of a Lyapunov function related to an active subsystem on the basis of whether the saturations occur or not. Then, a new iterative algorithm is designed to solve the matrix inequality and a SOF controller can be added. In the iterative linear matrix inequality (ILMI) algorithm, it is important not only to overcome the typical bilinear matrix inequality (BMI) problem of SOF, but also to solve the non-convex problem caused by state constraints. Finally, the availability and the applicability of the proposed method is shown by the application of a boost converter.

Discrete bilinear stochastic systems with time-varying delay: Stability analysis and control synthesis

In this paper, the problem of finite-time stability is studied for a class of networked predictive control systems with parameter uncertainties. Firstly, both the modelling uncertainties and the network-induced delays are considered. A networked predictive control scheme is proposed to actively compensate the network-induced delays. Secondly, a sufficient condition is given to ensure the finite-time stability of the augmented closed-loop system with time delay, where both bilinear matrix inequality and linear matrix inequality conditions are derived with the help of Lyapunov stability theorem. At the same time, an alternate algorithm is designed to obtain the gain matrices of observer and controller from bilinear matrix inequality and linear matrix inequality. Finally, a numerical example is given to confirm the feasibility of the proposed results.

Considers decentralized H/sub /spl infin// controller design problems for multi-channel linear time-invariant systems. Our interest is focused on dynamic output feedback, and our discussion concerns both continuous-time systems and discrete-time ones. The decentralized H/sub /spl infin// control problems are expressed as feasibility problems of bilinear matrix inequalities (BMIs) with respect to variables of a coefficient matrix defining the controller and a Lyapunov matrix. To deal with the BMIs, we propose to set the Lyapunov matrix as block diagonal appropriately according to the desired order of the controller so that the BMIs; are reduced to linear matrix inequalities (LMIs) which are sufficient to the BMIs but much more tractable.

This note is concerned with the static output feedback (SOF) H-infinity controller design for linear timeinvariant systems. A sufficient bilinear matrix inequality (BMI) condition is developed for finding a stabilizing static output feedback H-infinity controller. For the first time, a novel cone complementary linearization approach within the context of linear matrix inequalities (LMI) is proposed to investigate the feasibility of the stabilizing controller synthesis along with a minimized H-infinity attenuation rate. The proposed method requires neither any apriori assumption generally made on the input/output matrices nor any application of a coordinate transformation. An example is presented for the application of the proposed scheme.

The constrained Hinfin static output feedback control scheme is addressed for discrete-time with control constraints. A sufficient condition is presented for the static output feedback stabilization and Hinfin performance for linear systems. This condition is expressed as linear matrix inequality feasibility problems. By adding dissipation constraint to the mentioned condition, the problem of designing controller is then formulated as online constrained optimization problem. Closed-loop properties including stability and Hinfin performance are discussed in the framework of dissipation theory

Motivated by the potentially application merits of wireless networked control systems (WNCSs), this paper presents a network-based formation framework for multi-agent systems. First, we construct a discrete formation protocol by integrating 802.11b. Meanwhile, one agent is considered as the reference, and the other ones keep a desired formation with the reference via communication networks. Using Lyapunov stability theory, sufficient convergence conditions are derived, and the verification problem of the sufficient conditions can be transformed as a linear matrix inequality (LMI) feasibility problem. Solving this LMI feasibility problem, a networked-based feedback controller can be easily obtained. Finally, simulation studies are provided to demonstrate the effectiveness of the proposed method.

This paper is concerned with the control of systems composed of multiple coupled subsystems. In such architectures, communication between different local controllers is desired in order to achieve a better overall control performance. Any resultant improvement in control performance needs, however, to be significant enough to warrant the additional design complexity and higher energy consumption and costs associated with introducing communication channels between controllers. A practical distributed control design aims, therefore, to achieve an acceptable balance between minimising the use of communication between controllers and maximising the system-wide performance. In this article, a new approach to the problem of synthesising stabilising distributed control laws for discrete-time linear systems that balances performance and communication is presented. The approach employs a supervisory agent that, periodically albeit not necessarily at every sampling instant, solves an optimisation problem in order to synthesise a stabilising state feedback control law for the system. The online optimisation problem, which maximises sparsity of the control law while minimising an infinite-horizon performance cost, is formulated as a bilinear matrix inequality (BMI) problem; subsequently, it is then relaxed to a linear matrix inequality (LMI) problem, and (i) convergence to a solution as well as (ii) that early termination guarantees a feasible (but suboptimal) control law are proved. Stability of the closed-loop system under what is a switched control law is guaranteed by the inclusion of dwell-time constraints in the LMI problem. Finally, the efficacy of the approach is demonstrated through numerical simulation examples.

A theoretical framework is proposed to analyze the performance of active queue management (AQM) protocols in TCP-governed wireless networks. It is assumed that the TCP-governed sources operate in the linear-increase-multiplicative-decrease mode. A bottleneck network topology involving a single router and multiple users is examined and it is shown that the problem of synthesizing stabilizing AQM controllers is equivalent to that of solving a class of bilinear matrix inequality (BMI) problems. A series of such BMI formulations for a class of AQM controllers is presented and it is observed that some of these formulations can be recast as linear matrix inequality (LMI) formulations, which can be solved efficiently.

SummaryAn approach to find a static output feedback gain that makes the feedback system positive and minimizes the L1 gain is proposed. The problem of finding a static output feedback gain has 3 aspects: stabilizing the system, making the system positive, and then minimizing the L1 gain. Each subproblem is described by bilinear matrix inequality with respect to the feedback gain and the Lyapunov matrix or vector. Linear matrix inequality (LMI) that is sufficient to satisfy bilinear matrix inequality is derived using a convex‐concave decomposition, and the feedback gain sequence is calculated by an iterative solution of LMI. The sequence of the upper bounds on the design parameter is guaranteed to be monotonically nonincreasing for each algorithm. Similarly, 2 other LMIs are derived for each subproblem using another convex‐concave decomposition and PK iteration. The effectiveness of these algorithms is illustrated via several numerical examples.

International audience

This paper proposes the output feedback optimal guaranteed cost controller design method for uncertain piecewise linear systems based on the piecewise quadratic Lyapunov functions technique. By constructing piecewise quadratic Lyapunov functions for the closed‐loop augmented systems, the existence of the guaranteed cost controller for closed‐loop uncertain piecewise linear systems is cast as the feasibility of a set of bilinear matrix inequalities (BMIs). Some of the variables in BMIs are set to be searched by genetic algorithm (GA), then for a given chromosome corresponding to the variables in BMIs, the BMIs turn to be linear matrix inequalities (LMIs), and the corresponding non‐convex optimization problem, which minimizes the upper bound on cost function, reduces to a semidefinite programming (SDP) which is convex and can be solved numerically efficiently with the available software. Thus, the output feedback optimal guaranteed cost controller can be obtained by solving the non‐convex optimization problem using the mixed algorithm that combines GA and SDP. Numerical examples show the effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.

In this paper, in terms of Matrix Hadamard product a new control model is proposed for regulating connection coefficients of the state variables of the systems. It combines the traditional feedback compensation and the direct regulations for the connections of system states. The solution of control law to stabilize the systems via the regulations of connection coefficients can be obtained via a bilinear matrix inequality (BMI) involved Hadamard product. Under a certain conditions, we translate the BMI into a linear matrix inequality (LMI). Finally, we present some algebraic results when the matrices A <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> , A <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> have some special characters.

This paper presents a nonlinear control design method for robust stabilization and robust performance of linear differential inclusions. A recently introduced non-quadratic Lyapunov function, the convex hull quadratic function, is used for the construction of nonlinear state feedback laws. Design objectives include stabilization with maximal convergence rate, disturbance rejection with minimal reachable set and least /spl Lscr//sub 2/ gain. Conditions for stabilization and performances are derived in terms of bilinear matrix inequalities (BMIs), which cover the existing linear matrix inequality (LMI) conditions as special cases. Optimization problems with BMI constraints are formulated and solved effectively by combining the path-following algorithm and the direct iterative algorithm. The design results are guaranteed to be at least as good as the existing results obtained from LMI conditions. In most examples, significant improvements on system performances have been achieved, which demonstrate the advantages of using nonlinear feedback control over linear feedback control for linear differential inclusions. It is also observed through numerical computation that nonlinear control strategies may help to reduce control effort substantially.

An optimization problem related to bilinear matrix inequalities (BMIs) is considered. A branch-and-bound type global algorithm is obtained based on a linear matrix inequality (LMI)-relaxation and an upper bound of its worst case performance is derived. Taking account of activities of the relaxed problem, an improved algorithm is also proposed.