Chaotifying a linear time-invariant system by the state feedback controller and sawtooth function

Block-form control of linear time-invariant discrete-time systems defined over commutative rings

Many different types of adaptive or universal controllers", capable of dealing with a very broad range of linear time-invariant systems, have been proposed. One class of such controllers uses switching between a finite, or at least countable, number of fixed controllers until stability is detected. Such controllers are very attractive from a theoretical viewpoint, in providing stabilization and asymptotic performance for a broad class of plants. However, such controllers are also known to have very poor transient properties, due to the long time required to search for a stabilizing feedback. The key contribution of this paper is to introduce the "method of localization" which can greatly improve the speed of the search. The method is described for linear time-invariant discrete time systems of known nominal order, with disturbances and noise present. Analysis and simulations demonstrate the potential for greatly improved transient performance.

Interval observer design for unknown input estimation of linear time-invariant discrete-time systems

Decoupling of Discrete-time Dynamical Systems Through Input-Output Blending

This paper deals with the question of the existence of weak and strong common
\nquadratic Lyapunov functions (CQLFs) for stable discrete-time linear timeinvariant
\n(LTI) systems. The main result of the paper provides a simple characterisation
\nof pairs of such systems for which a weak CQLF of a given form exists
\nbut for which no strong CQLF exists. An application of this result to second
\norder discrete-time LTI systems is presented.

Optimal performance of discrete-time control systems based on network-induced delay

An Event-Triggered Watermarking Strategy for Detection of Replay Attacks

A discrete-time time-invariant linear system (DILS) is considered which has resulted from the discretization of a continuous-time time-invariant linear system (CILS) by the zero order hold. In this system, the system and input matrices are given by exp(AT) and $ where A and B are the system and input matrices of the CILS, and T is a sampling interval. Since they involve the matrix exponential, their computations are not easy. First, on the assumption that the Kalman canonical form of the CILS is sought, a formal Kalman canonical form of the DILS is determined. Second, with the use of this form and the decomposition of A into the projectors onto the generalized eigenspaces, an algorithm is presented which computes the system and input matrices of the DlLS.

Simultaneous global external and internal stabilization of linear time-invariant discrete-time systems subject to actuator saturation

This communication is concerned with stabilization via output static feedback of discrete-time linear time-invariant finite-dimensional systems. A new concept is introduced: output static stabilization in the relaxed sense. This (conservative) stabilization concept is defined so that it is characterized in terms of the discrete-time LQR problem. Properties, and alternative equivalent definitions of this new concept are analyzed. It is shown that for a particular class of plants, the stabilization problem in the above new sense can be cast as a convex programming problem (which moreover can be used as a tool for synthesis). A full characterization for the class of plants that are stabilizable in the above sense is presented. Important consequences of this characterization are somehow surprising. It is shown that the introduced new (conservative) stabilization concept is indeed much more important than it seems. The general problem of output static stabilization can be transformed into the stabilization problem in this new sense. A relationship between output static stabilizability and the discrete-time LQR problem is proved. Convex necessary and sufficient conditions, for joint stabilization (of multiple plants) in the above sense and for decentralized stabilization in the above sense, are presented.

Typical reason of traffic congestion within urban road traffic networks (URTNs), is that the distribution of traffic flows is unbalanced, i.e., occupancy of vehicles in some links is high, however there still exists much space being not utilized sufficiently, in other links. Motivated by this problem, the paper proposes a real-time signal control strategy, called the UTBC (Urban Traffic Balance Control, for short) strategy, under which traffic states within links can reach consensus, i.e., the network can realize the balanced distribution of traffic flows. First, a signal control model of URTNs based on basic conservation principle of vehicle flows is proposed, which is a discrete-time linear time-invariant control system, with control input being phase green-time durations. Furthermore, the state-feedback signal control law (i.e., the UTBC strategy), is proposed, such that the closed-loop signal control system can realize consensus. Moreover, ALINEA ramp metering algorithm is considered. At last, we illustrate joint applications of the UTBC and ALINEA strategies by conducting simulation tests for a real-world network in Wangjing District in Beijing. The simulation results show that the UTBC strategy is feasible and effective.

In this study, the mutual information between the state sequence and the measurements is proposed as an observability measure and this measure is analyzed in detail for linear time invariant discrete-time Gaussian systems. The following results are found as the two basic properties of the measure from the analyses; the unobservable states of the deterministic system have no effect on it. So the measure proposed here is an observability measure of observable states. Secondly, any observable part with no measurement uncertainty makes the measure infinite.

It is shown that a 2-D linear time-invariant discrete-time system could be bounded-input bounded-output (BIBO) unstable even if the 2-D system, which is implemented by finite word length, is free of overflow oscillations with zero input, according to a previous criterion for the absence of overflow oscillations in 2-D discrete-time systems. An improved criterion is presented to ensure both stability properties.

The main contribution of this paper is a generalization of the Box Theorem, which was originally introduced for the Hurwitz case, for determining the robust Schur-stability of linear time-invariant discrete-time control systems containing an interval plant. This generalization provides necessary and sufficient conditions for the stability of a family of closed-loop characteristic polynomials <(z) = Q1,(z)P1(z) +... + Qm(z)Pm(z), where the Qis are fixed (controller) and then Pis are interval (plant) polynomials whose coefficients vary within a prescribed interval. This method requires checking a set of prescribed segment polynomials whose number is considerably less than that of the edges required by the edge theorem. A summary of the robust Schur-stability of discrete-time interval polynomials is presented.

Robust filtering of linear time-invariant discrete-time uncertain systems is investigated through a new parameter dependent Lyapunov matrix procedure. Its main interest relies on the fact that the Lyapunov matrix used in stability checking does not appear in any multiplicative term with the uncertain matrices of the dynamic model. We show how to use such an approach to determine high performance H2 robust filters by solving a linear problem constrained by linear matrix inequalities (LMIs). The results encompass the previous works in the quadratic Lyapunov setting. Numerical examples illustrate the theoretical results.