Every normal linear system has a regular time-optimal synthesis
Exact decomposition of linear singularly perturbed -optimal control problem
Existence theorems for some optimal control problems
Exponentially discounted estimates and oscillations in linear controlled systems
Exterior algebra and invariant spaces of implicit systems: The Grassmann representative approach
External properness
In this paper, we revisit the structural concept of properness. We distinguish between the properness of the whole system, here called internal properness, and the properness of the “observable part” of the system. We give geometric characterizations for this last properness concept, namely external properness.
External reachability (reachability with pole assignment by p. d. feedback) for implicit descriptions
Externally and internally positive singular discrete-time linear systems
Notions of externally and internally positive singular discrete-time linear systems are introduced. It is shown that a singular discrete-time linear system is externally positive if and only if its impulse response matrix is non-negative. Sufficient conditions are established under which a single-output singular discrete-time system with matrices in canonical forms is internally positive. It is shown that if a singular system is weakly positive (all matrices E, A, B, C are non-negative), then it...
Externally and internally positive time-varying linear systems
The notions of externally and internally positive time-varying linear systems are introduced. Necessary and sufficient conditions for the external and internal positivities of time-varying linear systems are established. Moreover, sufficient conditions for the reachability of internally positive time-varying linear systems are presented.
Extracting second-order structures from single-input state-space models: Application to model order reduction
This paper focuses on the model order reduction problem of second-order form models. The aim is to provide a reduction procedure which guarantees the preservation of the physical structural conditions of second-order form models. To solve this problem, a new approach has been developed to transform a second-order form model from a state-space realization which ensures the preservation of the structural conditions. This new approach is designed for controllable single-input state-space realizations...
Falseness of the finiteness property of the spectral subradius
We prove that there exist infinitely may values of the real parameter α for which the exact value of the spectral subradius of the set of two matrices (one matrix with ones above and on the diagonal and zeros elsewhere, and one matrix with α below and on the diagonal and zeros elsewhere, both matrices having two rows and two columns) cannot be calculated in a finite number of steps. Our proof uses only elementary facts from the theory of formal languages and from linear algebra, but it is not constructive...
Fault-tolerant control strategy for actuator faults using LPV techniques: Application to a two degree of freedom helicopter
In this paper, a Fault Tolerant Control (FTC) strategy for Linear Parameter Varying (LPV) systems that can be used in the case of actuator faults is proposed. The idea of this FTC method is to adapt the faulty plant instead of adapting the controller to the faulty plant. This approach can be seen as a kind of virtual actuator. An integrated FTC design procedure for the fault identification and fault-tolerant control schemes using LPV techniques is provided as well. Fault identification is based...
Finite time stability and relative controllability of second order linear differential systems with pure delay
We first consider the finite time stability of second order linear differential systems with pure delay via giving a number of properties of delayed matrix functions. We secondly give sufficient and necessary conditions to examine that a linear delay system is relatively controllable. Further, we apply the fixed-point theorem to derive a relatively controllable result for a semilinear system. Finally, some examples are presented to illustrate the validity of the main theorems.
Fractional kalman filter algorithm for the states parameters and order of fractional system estimation
This paper presents a generalization of the Kalman filter for linear and nonlinear fractional order discrete state-space systems. Linear and nonlinear discrete fractional order state-space systems are also introduced. The simplified kalman filter for the linear case is called the fractional Kalman filter and its nonlinear extension is named the extended fractional Kalman filter. The background and motivations for using such techniques are given, and some algorithms are discussed. The paper also...
Fundamental theorem of proportional state feedback for descriptor systems
Fundamental theorem of state feedback: The case of infinite poles
Generalized synchronization-based partial topology identification of complex networks
In this paper, partial topology identification of complex networks is investigated based on synchronization method. We construct the response networks consisting of nodes with sim-pler dynamics than that in the drive networks. By constructing Lyapunov function, sufficient conditions are derived to guarantee partial topology identification by designing suitable controllers and parameters update laws. Several numerical examples are provided to illustrate the effectiveness of the theoretical results....
Generic properties of linear control systems depending on a parameter
Geometric methods in the theory of singular 2-D linear systems
-optimal rejection with preview: geometric constraints and dynamic feedforward solutions via spectral factorization
In this work, a feedforward dynamic controller is devised in order to achieve H2-optimal rejection of signals known with finite preview, in discrete-time systems. The feedforward approach requires plant stability and, more generally, robustness with respect to parameter uncertainties. On standard assumptions, those properties can be guaranteed by output dynamic feedback, while dynamic feedforward is specifically aimed at taking advantage of the available preview of the signals to be rejected, in...