1,421 research outputs found
Stability of switched linear differential systems
We study the stability of switched systems where the dynamic modes are
described by systems of higher-order linear differential equations not
necessarily sharing the same state space. Concatenability of trajectories at
the switching instants is specified by gluing conditions, i.e. algebraic
conditions on the trajectories and their derivatives at the switching instant.
We provide sufficient conditions for stability based on LMIs for systems with
general gluing conditions. We also analyse the role of positive-realness in
providing sufficient polynomial-algebraic conditions for stability of two-modes
switched systems with special gluing conditions
Convex computation of the region of attraction of polynomial control systems
We address the long-standing problem of computing the region of attraction
(ROA) of a target set (e.g., a neighborhood of an equilibrium point) of a
controlled nonlinear system with polynomial dynamics and semialgebraic state
and input constraints. We show that the ROA can be computed by solving an
infinite-dimensional convex linear programming (LP) problem over the space of
measures. In turn, this problem can be solved approximately via a classical
converging hierarchy of convex finite-dimensional linear matrix inequalities
(LMIs). Our approach is genuinely primal in the sense that convexity of the
problem of computing the ROA is an outcome of optimizing directly over system
trajectories. The dual infinite-dimensional LP on nonnegative continuous
functions (approximated by polynomial sum-of-squares) allows us to generate a
hierarchy of semialgebraic outer approximations of the ROA at the price of
solving a sequence of LMI problems with asymptotically vanishing conservatism.
This sharply contrasts with the existing literature which follows an
exclusively dual Lyapunov approach yielding either nonconvex bilinear matrix
inequalities or conservative LMI conditions. The approach is simple and readily
applicable as the outer approximations are the outcome of a single semidefinite
program with no additional data required besides the problem description
A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems
This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version
Aspects of Non-commutative Function Theory
We discuss non commutative functions, which naturally arise when dealing with
functions of more than one matrix variable
ââ optimization with spatial constraints
A generalized ââ synthesis problem where non-euclidian spatial norms on the disturbances and output error are used is posed and solved. The solution takes the form of a linear matrix inequality. Some problems which fall into this class are presented. In particular, solutions are presented to two problems: a variant of ââ synthesis where norm constraints on each component of the disturbance can be imposed, and synthesis for a certain class of robust performance problems
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