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This paper proposes a method for frequency-weighted discrete-time linear parameter varying (LPV) model reduction with bounded rate of parameter variation, using structurally balanced truncation with a priori (non-tight) upper error bounds for each fixed parameter. For systems with both input and output weighting filters, guaranteed stability of the reduced-order model is proved as well as existence...
Necessary and sufficient stability conditions are given for the existence of a continuous Lyapunov function for a semicontinuous, stochastic discrete-time system. The continuity of the Lyapunov function is linked to robustness of the stability property, which reduces to classical stability plus convergence for deterministic systems. The nature of the Lyapunov results are inspired by Lyapunov results...
This paper deals with stabilization of networked control systems (NCS) affected by uncertain time-varying delays and data packet dropouts. We point out that such network effects are likely to render the classical control Lyapunov function (CLF) method unfeasible, mainly due to the monotonic decreasing condition. To solve this problem we make use of a discrete-time equivalent of a control Lyapunov-Razumikhin...
In this paper we give conditions that a discrete time switched linear systems must satisfy if it is stable. We do this by calculating the mean and covariance of the set of matrices obtained by using all possible switches. The theory of switched linear systems has received considerable attention in the systems theory literature in the last two decades. However, for discrete time switched systems the...
This paper is concerned with the problem of receding horizon control of discrete-time systems subject to possibly unbounded random noise inputs, while satisfying hard bounds on the control inputs. We use a nonlinear feedback policy with respect to noise measurements and show that the resulting mathematical program has a tractable convex solution. Moreover, under the assumption that the zero-input...
Stabilizability of linear time invariant networked systems of general structure is studied with an observer-based approach. In the assumption of piecewise constant controls an average consensus network distributes input information to all agents enabling them to build local observers on the basis of which stabilizing gains are computed with recourse to standard centralized methodology. Stabilizability...
The stability of Boolean networks and the stabilization of Boolean control networks are investigated. Using semi-tensor product of matrices and the matrix expression of logic, the dynamics of a Boolean (control) network can be converted to a discrete time linear (bilinear) dynamics, called the algebraic form of the Boolean (control) network. They provide a framework for this study. Main results consist...
Model predictive control (MPC) is an on-line control technique originally developed for slow processes which makes an assessment between input effort and output error while respecting constraints on inputs and outputs. Due to improved computing power and algorithms, MPC is nowadays also applied to mechatronic systems. For these systems, achieving minimal settling time is the main concern, while the...
This paper studies the optimal tracking performance of multiple-input multiple-output (MIMO), finite dimensional, linear time-invariant discrete-time systems with a power-constrained additive white noise (AWN) channel in the feedback path. We adopt the tracking error power as a measure of the performance and examine the best achievable performance by all two-parameter stabilizing controllers. In the...
This paper investigates the optimality of the logarithmic quantizer on stabilization of linear systems. It is shown that a finite-level logarithmic quantizer can asymptotically achieve the well-known minimum average data rate for stabilizing an unstable MIMO linear discrete-time system. A time-sharing protocol is proposed to allocate bits to subsystems, each associated with an unstable eigenvalue...
We study certain difference equations arising in the stability analysis of Kalman filtering for a class of linear, discrete-time, possibly non-detectable systems with incorrect noise information. We obtain bounds for the solutions of these equations and the Riccati difference equation associated with the Kalman filter, under the assumption that the Riccati solution is bounded above and an assumption...
A computational method for stability analysis of discrete-time piecewise linear systems is presented. The method is based on combining the solutions to two separate problems: one is to obtain stabilizing switching sequences between linear dynamics, and the other is to obtain an increasing sequence of state-space partitions. Examples show that there are cases where the presented method is very useful.
This paper studies the stabilization problem for a class of networked control systems (NCSs) with communication constraints and random packet dropouts. The considered plant is equipped with multiple sensor nodes and actuator nodes. Only one of them can communicate with the controller at each transmission instant due to the communication constraints, and packet dropouts may occur at each transmission...
In this paper, we study the discrete-time nonlinear consensus protocols over both directed and undirected networks with fixed topology. First, the notions of (global/exponential) semistability are introduced for systems with a continuum of equilibria. In terms of (global/exponential) consensus defined based on the notion of semistability, we have derived convergence conditions for the general discrete-time...
Output-based feedback control of LPV systems is an important problem, as in practice it is rarely the case that the full state variable is available for feedback. In this paper we consider this problem in the case of discrete-time LPV systems for which the parameters are not exactly known, but only available with a finite accuracy or affected by noise during their measurement. The controllers are...
This paper is concerned with stability analysis of discrete-time networked control systems in the case where both input and output channels are characterized by a multiple-packet transmission policy. A necessary and sufficient condition for stability is obtained for known packet dropping probabilities. The issue of stability robustness of a system against packet dropping is discussed and addressed...
This paper investigates robust stability of discrete-time descriptor polytopic systems (DTDPSs for short). The concept of affine generalized quadratic stability, which has less conservatism than generalized quadratic stability, of DTDPSs is proposed. It not only investigates affine generalized quadratic stability of DTDPSs implies robust stability, but also presents criterions in terms of linear matrix...
Finite-time stability (FTS) requires that the state of a system does not exceed a certain bound during a specified time interval for given bound on the initial state. The concept of FTS introduced exogenous inputs is called finite-time boundedness (FTB). This paper gives necessary and sufficient conditions for FTB of linear time-varying discrete-time systems. The conditions are extensions of those...
In this paper a 2D systems setting is used to develop new results on iterative learning control for linear plants in the case when there are multiple reference signals. The algorithms for control law design are developed using a strong form of stability for discrete linear repetitive processes known as stability along the pass. The resulting design computations are in terms of linear matrix inequalities...
A limiting property of the matrix exponential is proven: For a real square matrix, where the log norm of the upper-left n by n block approaches negative infinity in a limiting process, the matrix exponential goes to zero in the first n rows and n columns. This property is useful for simplification of dynamic systems that exhibit modes with sufficiently different time scales; for example, in multi-loop...
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