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Our study proposes a data‐driven framework that identifies the level of functional simplicity of catchment's stormflow generation during dormant/growing seasons, using daily scale observations of streamflow and precipitation. We classify 619 rain‐dominated catchments across Canada, the United States, Great Britain, and Australia into three behavioral classes—simple, intermediate, and complex—based on the validity of (segmented) linear models in explaining the inter‐event relationship between precipitation volume and stormflow volume. Results reveal that simple stormflow generation behavior occurs at 108 catchments during dormant seasons with the linear model explaining most variability of inter‐event relationship between precipitation and stormflow volumes (median R2 of 0.81). These simple catchments are typically steep with wet/out‐of‐phase climate and strong precipitation persistence. The functional simplicity of simple catchments is further explored using spectral (coherency) analysis, which indicates the level of synchronicity between daily scale precipitation and streamflow time‐series. Simple catchments exhibit a strong coherency value at high frequencies, resembling the dynamic of a nearly Linear Time‐Invariant system. Indeed, the portion of precipitation volume that becomes stormflow tends to remain constant during dormant seasons, since the transfer function translating precipitation pulses to the streamflow hydrograph is nearly linear and time‐invariant. Complex catchments, in contrast, exhibit nonlinear relationships and time‐variant transfer functions, with weak coherency between precipitation and streamflow time‐series. Our results guide modeling frameworks to adjust the simplicity/complexity level with the catchment's “observation‐based” functional behavior. By synthesizing the causes/drivers and empirical equations relevant to simple stormflow behavior, our study contributes to the development of a unified hydrologic theory of stormflow generation. Plain Language Summary Catchments are often assumed to behave complexly during stormflow generation with time‐dependent and hysteretic functional behavior. This complexity challenges the synthesis of the “heap of facts” observed in diverse experimental catchments, hindering the development of a consistent body of hydrologic theory. Such synthesis is essential to develop (and regionalize) reliable models to predict and forecast hydrologic response, identify vulnerabilities to flood/drought, and conduct land‐use and climate‐change scenario analyses. Our results show that despite all within‐catchment complexities, many landscapes' wet climates, out‐of‐phase seasonality (with large time difference between precipitation and temperature peaks), and steep topographies could override small‐scale heterogeneities, resulting in a “simple” catchment‐scale functional behavior. Such functional simplicity is relatively more prevalent during dormant seasons than growing seasons. Simplicity is governed by linearity and stationarity of catchment functional dynamics. Identifying and synthesizing simple functional dynamics is a crucial first step in understanding non‐simple functional dynamics and, ultimately, in developing a generalizable theory of catchment hydrologic function applicable to catchments of different levels of simplicity/complexity worldwide. Key Points Dormant seasons' simple stormflow functionality is prevalent, occurring mostly along steep catchments with wet/out‐of‐phase climate Simple catchments transfer precipitation pulses into the streamflow hydrograph using a (nearly) time‐invariant transfer function during dormant seasons A flashier simple catchment with a faster decay rate transfers a larger portion of precipitation volume to stormflow volume

This paper presents the design and analysis of Switched Fractional Order Model Reference Adaptive Controllers (SFOMRAC) for Multiple Input Multiple Output (MIMO) linear systems with unknown parameters. The proposed controller uses adaptive laws whose derivation order switches between a fractional order and the integer order, according to a certain level of control error. The switching aims to use fractional orders when the control error is larger to improve transient response and system performance during large disturbed states, and to obtain smoother control signals, leading to a better control energy usage. Then, it switches to the integer order when the control error is smaller to improve steady state. Boundedness of all the signals in the scheme is analytically proved, as well as convergence of the control error to zero. Moreover, these properties are extended to the case when system states are affected by a bounded non-parametric disturbance. Simulation studies are carried out using different representative plants to be controlled, showing that fractional orders and switching error levels can be found in most of the cases, such as when SFOMRAC achieves a better balance among control energy and system performance than the non-switched equivalent strategies.

Human behavior and affect is inherently a dynamic phenomenon involving temporal evolution of patterns manifested through a multiplicity of non-verbal behavioral cues including facial expressions, body postures and gestures, and vocal outbursts. A natural assumption for human behavior modeling is that a continuous-time characterization of behavior is the output of a linear time-invariant system when behavioral cues act as the input (e.g., continuous rather than discrete annotations of dimensional affect). Here we study the learning of such dynamical system under real-world conditions, namely in the presence of noisy behavioral cues descriptors and possibly unreliable annotations by employing structured rank minimization. To this end, a novel structured rank minimization method and its scalable variant are proposed. The generalizability of the proposed framework is demonstrated by conducting experiments on 3 distinct dynamic behavior analysis tasks, namely (i) conflict intensity prediction, (ii) prediction of valence and arousal, and (iii) tracklet matching. The attained results outperform those achieved by other state-of-the-art methods for these tasks and, hence, evidence the robustness and effectiveness of the proposed approach.

Given a Laurent polynomial F ∈ C [ z 1 ± 1 , … , z n ± 1 ] , its amœba A F is the image by z = ( z 1 , … , z n ) ∈ ( C ∗ ) n ⟼ ( log | z 1 | , … , log | z n | ) ∈ R n of the algebraic zero set V ( F ) = { z ∈ ( C ∗ ) n ; F ( z ) = 0 } of the complex torus T n : = ( C ∗ ) n . We relate here the question of the BIBO stability of a multilinear discrete time invariant system with a regular transfer function G ( z 1 , . . . , z n ) / F ( z 1 , … , z n ) , where F , G ∈ C [ z 1 , . . . , z n ] are coprime or more precisely structural stability , with the geometrical study of the amœba A F . A criterion for strong and weak structural stability is expressed in terms of the position of 0 = ( 0 , … , 0 ) ∈ R n with respect to the amœba A F . Then we propose a Monte-Carlo integration based algorithm in order to test the structural stability of a given such system. The proposed algorithm is not limited by the curse of dimensionality, as opposed to the state-of-the-art methods: It can be applied to any number of variables n . Several illustrative examples are presented and discussed.

This paper discusses model order reduction of linear time-invariant (LTI) systems over limited frequency intervals within the framework of balanced truncation. Two new frequency-dependent balanced truncation methods are developed, one is single-frequency (SF)-type frequency-dependent balanced truncation to cope with the cases that only a single dominating point of the operating frequency interval is pre-known, and the other is interval-type frequency-dependent balanced truncation to deal with the case that both the upper and lower bounds of the relevant frequency interval are known a priori. Error bounds for both approaches are derived to estimate the approximation error over a pre-specified frequency interval. In contrast to other error bounds for frequency-weighted or frequency-limited balanced truncation, these bounds are given specifically for the interval under consideration and are thus often sharper than the global bounds for previous methods. We show that the new methods generally lead to good in-band approximation performance, and at the same time provide accurate error bounds under certain conditions. Examples are included for illustration.

From the perspective of the importance of the fractional-order linear time-invariant (FoLTI) system in plenty of applied science fields, such as control theory, signal processing, and communications, this work aims to provide certain generic solutions for commensurate and incommensurate cases of these systems in light of the Adomian decomposition method. Accordingly, we also generate another general solution of the singular FoLTI system with the use of the same methodology. Several more numerical examples are given to illustrate the core points of the perturbations of the considered singular FoLTI systems that can ultimately generate a variety of corresponding solutions.

The author offers a power-efficient multichannel low-pass filter for digital image processing based on the cascade multiple accumulate finite impulse response (CMFIR) structure in this study. The CMFIR filter was created using the outputs of a linear time-invariant system (LTI), which was built using a cascaded integrator comb (CIC) and a MAC low-pass filter. The sample rate convertor based on CIC filters effectively conducts decimation or interpolation. The sample rate convertor with the CIC filter can only accommodate narrowband transmissions and so cannot be utilized for wideband signals. The MAC architecture-based sample rate convertor is a good solution for high-bandwidth signals, but it uses more resources like registers and flip-flops, which increases power consumption. Here, the CMFIR low-pass filter acts as an interpolator, introducing a sample to boost the image's resolution. CMFIR is a useful tool for addressing the issue of aliasing during sampling. In addition, the genetic algorithm was used to increase the filter's resource utilization and power consumption efficiency.

This contribution deals with the static output feedback problem of linear time-invariant systems. This is still an area of active research, in contrast to the observer-based state feedback problem, which has been solved decades ago. We consider the formulation and solution of static output feedback design problems using quantifier elimination techniques. Stabilization as well as more specified eigenvalue placement scenarios are the focus of the paper.

In this paper, we consider the problem, usual in analog signal processing, to find a continuous linear time-invariant system related to a linear differential equation \\[P(D)x = Q(D)f\\], i.e. a system \\[ L\\] such that for every input signal f yields an output \\[ L(f)\\] which verifies \\[P(D) L(f ) = Q(D)f\\]. We give a systematic theoretical analysis of the existence and uniqueness of such systems (both causal and non-causal ones) defined on \\[L^p\\] functions and \\[ D'_L^p\\] distributions (input spaces which include signals with not necessarily left-bounded support), for every p. More precisely, by finding all their possible impulse responses, we characterise all these systems apart two pathologies arising when \\[p = ınfty \\]. Finally, we give necessary and sufficient conditions on P, Q for causality and stability of the systems. As an application, we consider the problem of finding the inverse of a causal continuous linear time-invariant system, defined on \\[L^p\\], related to a simple differential equation. We also show a digital simulation of this inverse system.

The paper studies input and state observability (ISO) of discrete-time linear time-invariant network systems whose dynamics are affected by unknown inputs. More precisely, we aim at reconstructing the initial state and the sequence of unknown inputs from the system outputs, and we will use the term ISO when the input reconstruction is possible with delay one, namely the inputs up to time k−1 and the states up to time k can be obtained from the outputs up to time k, while the term unconstrained ISO will refer to the case where there is some arbitrary delay in the input reconstruction. We focus on the problem of s-structural ISO (resp. s-structural unconstrained ISO) wherein the objective is to find conditions such that for all system matrices that carry the same network structure, the resulting system is ISO (resp. unconstrained ISO). We provide first a graphical characterization for s-structural unconstrained ISO, and subsequently, sufficient conditions and necessary conditions for s-structural ISO. For the latter, under the assumption of zero feedthrough, these conditions coincide and characterise ISO. The conditions presented are in terms of existence of suitable uniquely restricted matchings in bipartite graphs associated with the structured system. In order to test these conditions, we present polynomial-time algorithms. Finally, we discuss an equivalent reformulation of the main conditions in terms of coloring algorithms as in the literature of zero forcing sets.