1,720,976 research outputs found
Delay-independent conditions of exponential ISS for linear time-varying delay differential systems
No full textThis work focuses on linear continuous-time systems with time-varying delays, in the general case of time-varying matrices. Initially, we explore the case of positive systems within this class and introduce two distinct delay-independent conditions of exponential input-to-state stability. Moreover, we provide guaranteed exponential convergence rates for such conditions, explicitly stating the ISS gains. Then, we extend our analysis to systems without sign constraints, adopting a state-bounding approach that takes advantage of the properties of positive systems. Due to the time-varying nature of the systems, all proposed conditions are in terms of an infinite number of inequalities. Hence, implementation issues are discussed and significant special cases in which the conditions can be cast into a linear programming problem of finite dimension are presented
Some Remarks on the Stability of Time-Varying Discrete-Time Positive Delay Systems
No full textThis paper illustrates some remarkable properties of linear time-varying discrete-time positive systems with delays. First, we discuss how a well known property of positive delay systems with time-invariant matrices, namely the equivalence among delay-dependent and delay-independent stability, does not generalize to positive delay systems when the system matrices are time-varying. Then, we illustrate how a stability analysis based on the existence of linear co-positive Lyapunov functions on the zero-delay system and on its dual produces a remarkable dissimilarity to what happens in the time-invariant case: the dual condition is sufficient to prove delay-independent stability, whereas the primal is not even a stability condition. Implications and further results are discussed
First-moment stability of Markov Jump Linear Systems with homogeneous and inhomogeneous transition probabilities
No full textThis work provides 1-moment stability conditions for discrete-time Markov Jump Linear Systems under time-homogeneous and time-inhomogeneous transition probabilities. For the latter, we further address the polytopic switching case. The analysis is carried out leveraging the comparison principle and the theory of positive systems, without nevertheless limiting the overall analysis to the latter. We provide sufficient stability conditions that only involve non-negative matrices and can be checked via linear programming
Filtering Discrete-Time Systems with Multiplicative Noise in L2 Spaces with Applications
No full textIn this work we adopt a novel formulation of the distributed parameters recursive filter for discrete-time systems evolving in spaces to widen the class of systems that can be processed by a state estimation algorithm. Starting from a rigorous definition of Kronecker algebra on spaces that involves both elements and bounded operators of , we provide a computationally efficient solution in the case of linear systems with multiplicative noises. We illustrate the potential application of the approach by developing a case-study concerning the conceptual design of a distributed thermo-couple in the presence of the Nyquist-Johnson noise
Control System-Oriented MIMO Over-the-Air Computing
Get PDFThis paper applies the MIMO over-the-air computation (MIMO-AirComp) technique to compute the control signal of a distributed control system, including state estimation. The control-based target function is expressed as a nomographic function and efficiently computed through the wireless channel with suitable function decomposition. The proposed scheme leverages local pre-processing at the individual sensor, aggregation through the multiple access channel, and post-processing at the controller to compute the control-oriented nomographic function. We analyze the performance of our proposed scheme in terms of the time delay and computation error compared to a state-of-the-art MIMO time-division multiple access scheme by means of Monte Carlo simulations. Numerical results indicate that the proposed scheme considerably improves control performance, particularly in noisy networks that rely on a large number of wireless sensors, with low complexity for resource-constrained scenarios
Stability analysis of switched ARX models and application to learning with guarantees
No full textThe main subject of this work is the stability analysis of Switched Auto-Regressive models with eXogenous inputs (SARX), which constitute a reference class for switched and hybrid system identification. The work introduces novel conditions for the arbitrary switching stability of multiple-input multiple-output SARX models which exploit the peculiar structure of their state-space realization. The analysis relies on the properties of block companion matrices, and partly leverages results from the theory of non-negative matrices, without nevertheless asking for an input–output positive behavior of the model. The novel stability conditions have a simple formulation in terms of linear co-positive common Lyapunov functions, and come at a remarkably low computational cost, being solvable by Linear Programming. The low computational burden is particularly attractive in an identification context, as it allows to efficiently constrain learning procedures in order to obtain SARX models with stability guarantees. The latter is itself a contribution of the work, as it fills a gap in the literature on the estimation of SARX models. The results are validated on a particular learning technique based on Regression Trees – a well known machine learning algorithm – which has shown remarkable accuracy in experimental environments
Adaptive Mixture Model Reduction based on the Composite Transportation Dissimilarity
No full textProviding efficient yet accurate statistical models is a challenging problem in many applications. When elementary models are not sufficiently descriptive, mixtures of densities can be used. A complexity management issue arises when mixture models are employed: the number of components should be a trade-off between the complexity and the accuracy of the model. However, in general, it is not obvious how to determine the right number of mixture components for a specific application. In a previous work, theoretical foundations to address such a topic have been laid, grounded on the use of the Composite Transportation Dissimilarity between mixtures, and a preliminary criterion to manage the complexity of a mixture model has been proposed. In this paper, additional theoretical insights are provided that allow to formulate a novel adaptive mixture reduction algorithm. Numerical tests show that in most cases the new algorithm constitutes a significant improvement over the previous one
Filtering Discrete-Time Systems With Multiplicative Noise in L-2 Spaces With Applications
Get PDFIn this work we adopt a novel formulation of the distributed parameters recursive filter for discrete-time systems evolving in L-2 spaces to widen the class of systems that can be processed by a state estimation algorithm. Starting from a rigorous definition of Kronecker algebra on L-2 spaces that involves both elements and bounded operators of L-2, we provide a computationally efficient solution in the case of linear systems with multiplicative noises. We illustrate the potential application of the approach by developing a case-study concerning the conceptual design of a distributed thermo-couple in the presence of the Nyquist-Johnson noise
Stability analysis of coupled differential-difference systems with multiple time-varying delays: a positivity-based approach
No full textThis work introduces novel results on linear coupled differential-difference systems with multiple time-varying delays. First, necessary and sufficient conditions for the positivity and delay-independent asymptotic stability of such systems are introduced. Then, exploiting the Internally Positive Representation technique, we show how such stability results can be systematically exported to non-positive systems of the same class, yielding novel explicit sufficient conditions for their delay-independent stability. As a consequence, novel stability results on neutral-type systems, differential systems, and continuous-time difference systems with multiple delays are also obtained
On the stability of switched arx models, with an application to learning via regression trees
Get PDFThis work studies the stability properties of Switched AutoRegressive eXogenous (SARX) models subject to arbitrary switching sequences. We provide necessary and sufficient conditions for the arbitrary switching stability of multiple-input, single-output SARX models under nonnegativity constraints, and sufficient-only conditions removing sign constraints. The conditions are equivalentlv formulated on state-space representations of SARX models, due to their influential use in designing control strategies. As an application of the aforementioned results, we propose a novel algorithm for the identification of switched models with stability guarantees via Regression Trees, a powerful machine learning technique
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