LMI based output PS control design for discrete-time linear MIMO systems

The paper is concerned with the problem of designing PI output feedback control laws for linear time-invariant systems. Since this problem is generally stated as a bilinear optimization problem, using standard form of Lyapunov function and symmetric positive definite slack matrices, an enhanced algorithm is introduced with incidence of a scalar tuning parameter. The solution, obtained through linear matrix inequalities and equalities formulation, also unifies the control law design LMI-based procedure. The results, offering the conditions of PI output controller existence, are illustrated with numerical examples to note effectiveness and applicability of the considered approach.

A method for computing time-varying dynamic output feedback controllers for discrete-time linear systems subject to input saturation is proposed. The method is based on a locally valid polytopic representation of the saturation term. From this representation, it is shown that, at each sampling time, the matrices of the stabilising time-varying controller can be computed from the current system output and from constant matrices obtained as a solution of some matrix inequalities. Linear matrix inequality-based optimisation problems are therefore proposed in order to compute the controller aiming at the maximisation of the basin attraction of the closed-loop system, as well as aiming at ensuring a level of ℒ2 disturbance tolerance and rejection.

The paper offers mingling conditions for the interposed H2/H∞ control design for linear discrete-time systems. The goal is to design the feedback control which guarantees bounded H2 performance index and H∞ norm attenuation. Analyzing criteria observances given on a joined H2/H∞ control law, the task is formulated as a feasible problem subject to convex constraints expressed by a system of linear matrix inequalities. The effectiveness and pertinence of the interposed control strategy are demonstrated by results of a numerical example.

Periodic event-triggered state-feedback control for discrete-time linear systems

The problem of output feedback variable control of discrete-time linear systems with unmatched uncertainties is studied in this paper. The output feedback control doesn't need state available and estimated state. First, the sliding surface is designed by using linear matrix inequality (LMI) technique when there exists the unmatched uncertainties. The sufficient condition for the existence of stable sliding surface is derived in terms of LMIS. Then the design of sliding mode control is presented according to the reachability condition. Finally, an illustrative example is presented to show the feasibility and effectiveness of the proposed method.

In this paper, we present an approach for designing structural constrained controllers for discrete-time linear systems, based on a new stabilizability property of the Riccati equation solution. First, the feedback stabilization problem under a general structural constraint is considered and a simple numerical procedure to solve it is presented. Special attention is given to the output feedback stabilization problem, for which sufficient conditions for the existence and convergence toward a stabilizing matrix are provided. Some examples are solved and comparisons with other methods available in the literature are made.

This letter is concerned with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${H}_{2}$ </tex-math></inline-formula> control of discrete-time linear systems with dynamics determined by an independent and identically distributed (i.i.d.) process. A definition of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${H}_{2}$ </tex-math></inline-formula> norm is first discussed for the class of systems. Then, a linear matrix inequality (LMI) condition is derived for the associated performance analysis, which is tractable in the sense of numerical computation. The results about analysis are also extended toward state-feedback controller synthesis.

A Note on Stabilizing and Time-Optimal Controllers for Discrete-Time Linear Systems with Positive Controls

In this paper, stabilizing problems in control design are addressed for linear discrete-time systems, reflecting equality constraints tying together some state variables. Based on an enhanced representation of the bounded real lemma for discretetime systems, the existence of a state feedback control for such conditioned stabilization is proven, and an LMI-based design procedure is provided. The control law gain computation method used circumvents generally an ill-conditioned singular design task. The principle, when compared with previously published results, indicates that the proposed method outperforms the existing approaches, guarantees feasibility, and improves the steady-state accuracy of the control. Furthermore, better performance is achieved with essentially reduced design effort. The approach is illustrated on simulation examples, where the validity of the proposed method is demonstrated using one state equality constraint.

Symmetric positive definite (SPD) matrices used as feature descriptors in image recognition are usually high dimensional. Traditional manifold learning is only applicable for reducing the dimension of high-dimensional vector-form data.For high-dimensional SPD matrices, directly using manifold learning algorithms to reduce the dimension of matrix-form data is impossible. The SPD matrix must first be transformed into a long vector, and then the dimension of this vector must be reduced. However, this approach breaks the spatial structure of the SPD matrix space. To overcome this limitation, we propose a new dimension reduction algorithm on SPD matrix space to transform high-dimensional SPD matrices into low-dimensional SPD matrices. Our work is based on the fact that the set of all SPD matrices with the same size has a Lie group structure, and we aim to transform the manifold learning to the SPD matrix Lie group. We use the basic idea of the manifold learning algorithm called locality preserving projection (LPP) to construct the corresponding Laplacian matrix on the SPD matrix Lie group. Thus, we call our approach Lie-LPP to emphasize its Lie group character. We present a detailed algorithm analysis and show through experiments that Lie-LPP achieves effective results on human action recognition and human face recognition.

This paper deals with the problem of designing low sensitivity memory H ∞ state-feedback controllers for linear discrete-time systems with time delay. The time-delay factors are known constant scalar. The aim of this paper is to design a memory low sensitivity sate feedback control law such that the closed-loop system is asymptotically stable for all admissible time-delays and multiplicative controller coefficient variations in the framework of coefficient sensitivity theory. A new sufficient condition based on linear matrix inequality (LMI) technique for the existence of such controllers is formulated.

This note investigates the problem of output feedback H∞ control for linear discrete-time systems. Three types of H∞ controllers are considered, namely, static output feedback controllers, dynamic output feedback controllers, and observer-based output feedback controllers. New design conditions for the three type of output feedback controllers are introduced in terms of unified linear matrix inequality (LMI) representations, which guarantee the prescribed H∞ performances of the closed-loop systems. In contrast to the existing LMI conditions for designing the output feedback H∞ controllers, the improvement of the proposed results over the existing ones is shown by theoretical proof and numerical example.

To estimate the growth rate of matrix products $A_{n}··· A_{1}$ with factors from some set of matrices $\mathscr{A}$, such numeric quantities as the joint spectral radius $ρ(\mathscr{A})$ and the lower spectral radius $\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over \rho } (\mathscr{A})$ are traditionally used. The first of these quantities characterizes the maximum growth rate of the norms of the corresponding products, while the second one characterizes the minimal growth rate. In the theory of discrete-time linear switching systems, the inequality $ρ(\mathscr{A})&lt;1$ serves as a criterion for the stability of a system, and the inequality $\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\smile$}} \over \rho } (\mathscr{A})&lt;1 $ as a criterion for stabilizability.Given a set $\mathscr{A}$ of $N×M$ matrices and a set $\mathscr{B}$ of $M×N$ matrices. Then, for matrix products $A_{n}B_{n}··· A_{1}B_{1}$ with factors $A_{i}∈\mathscr{A}$ and $B_{i}∈\mathscr{B}$, we introduce the quantities $μ(\mathscr{A},\mathscr{B})$ and $η(\mathscr{A},\mathscr{B})$, called the lower and upper minimax joint spectral radius of the pair $\{\mathscr{A},\mathscr{B}\}$, respectively, which characterize the maximum growth rate of the matrix products $A_{n}B_{n}··· A_{1}B_{1}$ over all sets of matrices $A_{i}∈\mathscr{A}$ and the minimal growth rate over all sets of matrices $B_{i}∈\mathscr{B}$. In this sense, the minimax joint spectral radii can be considered as generalizations of both the joint and lower spectral radii. As an application of the minimax joint spectral radii, it is shown how these quantities can be used to analyze the stabilizability of discrete-time linear switching control systems in the presence of uncontrolled external disturbances of the plant.

This paper presents synthesis procedures for the design of both robust and gain-scheduled H∞ static output feedback controllers for discrete-time linear systems with time-varying parameters. The parameters are assumed to vary inside a polytope and have known bounds on their rate of variation. The geometric properties of the polytopic domain are exploited to derive a finite set of linear matrix inequalities that consider the bounds on the rate of variation of the parameters. A numerical example illustrates the proposed approach.

The goal of this paper is to study the switched stochastic control problem of discrete-time linear systems with multiplicative noises. We consider both the quadratic and the H∞ criteria for the performance evaluation. Initially we present a sufficient condition based on some Lyapunov–Metzler inequalities to guarantee the stochastic stability of the switching system. Moreover, we derive a sufficient condition for obtaining a Metzler matrix that will satisfy the Lyapunov–Metzler inequalities by directly solving a set of linear matrix inequalities, and not bilinear matrix inequalities as usual in the literature of switched systems. We believe that this result is an interesting contribution on its own. In the sequel we present sufficient conditions, again based on Lyapunov–Metzler inequalities, to obtain the state feedback gains and the switching rule so that the closed loop system is stochastically stable and the quadratic and H∞ performance costs are bounded above by a constant value. These results are illustrated with some numerical examples.