Matheus Souza

Discrete-Time Switched Linear Systems State Feedback Design With Application to Networked Control

This technical note addresses the state feedback switched control design problem for discrete-time switched linear systems. More specifically, the control goal is to jointly design a set of state feedback gains and a state dependent switching function, ensuring H2 and H∞ guaranteed performance. The conditions are based on Lyapunov or Riccati-Metzler inequalities, which allow the derivation of simpler alternative conditions that are expressed as LMIs whenever a scalar variable is fixed. The theoretical results are well adapted to deal with the self-triggered control design problem, where the switching rule is responsible for the scheduling of multiple sampling periods, to be considered in the communication channel in order to improve performance. This method is compared to others from the literature. Examples show the validity of the proposed technique in both contexts, switched and networked control systems.

On an LMI approach to optimal sampled-data state feedback control design

The literature presents a large number of interesting and useful results on sampled-data systems. In this paper, we deal with control design problems for this class of systems following a different route. The novelty is that the optimal and state feedback control design problems for sampled-data linear systems are solved in a unified and direct manner through linear matrix inequalities. To this purpose, the solution to a special two-point boundary value problem is used to verify the stability and to evaluate the performance of the closed-loop system. These results are then generalised to cope with non-uniform data rates. The theory is illustrated by means of simple examples borrowed from the literature.

State feedback switched control of discrete-time switched linear systems with application to networked control

This paper treats the state feedback switched control design problem for discrete-time switched linear systems. More specifically, the control goal is to design a set of state feedback gains together with a state dependent switching function assuring stability and H2, H∞ performance indexes. The conditions are based on Lyapunov or Riccati-Metzler inequalities which although are difficult to solve for a large number of subsystems, allow the derivation of simpler alternative conditions expressed by LMIs whenever a scalar variable is fixed. This theory is well adapted to treat an important networked control problem known as discrete-time self-triggered control design problem, where the switching rule is responsible for the scheduling of the sampling periods to be considered in the communication channel at each sampling time instant in order to improve performance. This method is compared theoretically with others from literature. Academical examples are used for comparisons and to show the validity of the proposed technique in both contexts, switched and networked control systems.

Self-triggered linear quadratic Networked Control

This paper deals with Networked Control Systems (NCS) design, under the constraint of limited bandwidth on the communication channel. A linear quadratic regulator for a fixed sampling period is solved and this result is used for the development of H2 and H∞ performance indexes, yielding to the statement and solution of H2 and H∞ optimal control problems. Finally, a self-triggered controller is designed with a switched system approach in order to improve performance. Examples are presented to illustrate the validity of the theory.

ℋ2 dynamic output feedback for local sensor – remote actuator networks

This paper addresses the dynamic output feedback control design problem for limited bandwidth and sampled-data dynamical systems, under the so-called local sensor – remote actuator setting. As a first approach, a suboptimal solution to the periodic sampled-data control problem is developed and it is shown that this solution presents the celebrated separation property. Based on this result, we provide two more general designs, which are well-adapted to practical applications in limited bandwidth networked environments. The first one is a robust controller, in which the data rate is a bounded, unknown and time-varying variable. The second one is a self-triggered controller, which improves the closed-loop performance by adequately choosing the sampling instants. Several examples validate the developed theory and point out its main potentialities.

ℋ 2 state feedback sampled-data control for Markov Jump Linear Systems

This paper is entirely devoted to analyzing the ℋ2 optimal state feedback sampled-data control design problem for Markov Jump Linear Systems. Our propose is to search for a solution to this problem by imbedding it in a more general class of dynamical systems, which we call Hybrid Markov Jump Linear System (HMJLS). In this new and wide context, we show how to calculate a sampled-data state feedback control that minimizes the ℋ2 performance index associated to the closed-loop system from the solution of a specific two-point boundary value problem. This result is adapted to provide optimal control conditions based on linear matrix inequalities (LMIs). The theory is illustrated by means of an academical example.

Switching Controller Design With Dwell-Times and Sampling

We consider the problem of obtaining state dependent switching strategies for switching linear time-invariant systems which satisfy prespecified dwell-time constraints. Continuous-time strategies which yield exponential stability and a guaranteed level of performance are presented. We also consider discrete-time strategies in which the sampling time is independent of the dwell-times. A numerical example is included to validate the developed theory.

Discretisation of sparse linear systems: An optimisation approach

Abstract This paper addresses the discretisation problem for sparse linear systems. Classical methods usually destroy sparsity patterns of continuous-time systems. We develop an optimisation procedure that yields the best approximation to the discrete-time dynamical matrix with a prescribed sparsity pattern and subject to stability and other constraints. By formulating this problem in an adequate manner, tools from convex optimisation can be then applied. Error bounds for the approximation are provided for special classes of matrices. Numerical examples are included.

On Analysis and Design of Discrete-Time Constrained Switched Systems

ABSTRACT This paper presents novel design techniques for discrete-time constrained switched systems. Two problems are considered: the first one is centred at determining a set of switching rules for which the system is unconditionally stable; the second one focuses on the design of a stabilising state-dependent switching function that is subject to structural constraints. Convex optimisation is the kernel of the devised procedures and, thus, these techniques are computationally viable.

A Note on Recursive Schur Complements, Block Hurwitz Stability of Metzler Matrices, and Related Results

It is known that the stability of a Metzler matrix can be characterized in a Routh–Hurwitz-like fashion based on a recursive application of scalar Schur complements [1]. Our objective in this brief note is to show that recently obtained stability conditions are equivalent statements of this result and can be deduced directly therefrom using only elementary results from linear algebra. Implications of this equivalence are also discussed and several examples are given to illustrate potentially interesting system-theoretic applications of this observation.