Time-local formulation and identification of implicit Volterra models by use of diffusive representation

We present a time-continuous identification method for nonlinear dynamic Volterra models of the form HX=f(u,X)+v with H, a causal convolution operator. It is mainly based on a suitable parameterization of H deduced from the so-called diffusive representation, which is devoted to state representations of integral operators. Following this approach, the complex dynamic nature of H can be summarized by a few numerical parameters on which the identification of the dynamic part of the model will focus. The method is validated on a physical numerical example.     

A parametric periodic Lyapunov equation with application in semi-global stabilization of discrete-time periodic systems subject to actuator saturation

This paper is concerned with semi-global stabilization of discrete-time linear periodic systems subject to actuator saturation. Provided that the open loop characteristic multipliers are within the closed unit circle, a low gain feedback design approach is proposed to solve the problem by state feedback. Our approach is based on the solution to a parametric discrete-time periodic Lyapunov equation. The proposed approaches not only generalize the corresponding results for time-invariant systems to periodic systems, but also reveal some important intrinsic properties of this class of periodic matrix equations. A numerical example is worked out to illustrate the effectiveness of the proposed approaches.     

Robustness analysis of genetic regulatory networks affected by model uncertainty

A fundamental problem in systems biology consists of investigating robustness properties of genetic regulatory networks (GRNs) with respect to model uncertainty. This paper addresses this problem for GRNs where the coefficients are rationally affected by polytopic uncertainty, and where the saturation functions are not exactly known. First, it is shown that a condition for ensuring that the GRN has a globally asymptotically stable equilibrium point for all admissible uncertainties can be obtained in terms of a convex optimization problem with linear matrix inequalities (LMIs), hence generalizing existing results that mainly consider only the case of GRNs where the coefficients are linearly affected by the uncertainty and the regulatory functions are in SUM form. Second, the problem of estimating the worst-case convergence rate of the trajectories to the equilibrium point over all admissible uncertainties is considered, and it is shown that a lower bound of this rate can be computed by solving a quasi-convex optimization problem with LMIs. Third, the paper considers the problem of estimating the set of uncertainties for which the GRN has a globally asymptotically stable equilibrium point. This problem is addressed, first, by showing how one can compute estimates with fixed shape by solving a quasi-convex optimization problem with LMIs, and second, by deriving a procedure for computing estimates with variable shape. Numerical examples illustrate the use of the proposed techniques.     

Interval observers for linear time-invariant systems with disturbances

It is shown that, for any time-invariant exponentially stable linear system with additive disturbances, time-varying exponentially stable interval observers can be constructed. The technique of construction relies on the Jordan canonical form that any real matrix admits and on time-varying changes of coordinates for elementary Jordan blocks which lead to cooperative linear systems. The approach is applied to detectable linear systems.     

Stabilizing composite control for a class of linear systems modeled by singularly perturbed Ito differential equations

In this paper, the problem of robust H_∞ control is investigated for sampled-data systems with probabilistic sampling. The parameter uncertainties are time-varying norm-bounded and appear in both the state and input matrices. For the simplicity of technical development, only two different sampling periods are considered whose occurrence probabilities are given constants and satisfy Bernoulli distribution, which can be further extended to the case with multiple stochastic sampling periods. By applying an input delay approach, the probabilistic sampling system is transformed into a continuous time-delay system with stochastic parameters in the system matrices. By linear matrix inequality (LMI) approach, sufficient conditions are obtained, which guarantee the robust mean-square exponential stability of the system with an H_∞ performance. Moreover, an H_∞ controller design procedure is then proposed. An illustrative example is included to demonstrate the effectiveness of the proposed techniques.     

Attainability of the minimum data rate for stabilization of linear systems via logarithmic quantization

This paper investigates the attainability of the minimum average data rate for stabilization of linear systems via logarithmic quantization. It is shown that a finite-level logarithmic quantizer suffices to approach the well-known minimum average data rate for stabilizing an unstable linear discrete-time system under two basic network configurations. In particular, we derive explicit finite-level logarithmic quantizers and the corresponding controllers to approach the minimum average data rate.     

Approaches to extended non-quadratic stability and stabilization conditions for discrete-time Takagi–Sugeno fuzzy systems

This paper provides simple and effective linear matrix inequality (LMI) characterizations for the stability and stabilization conditions of discrete-time Takagi–Sugeno (T–S) fuzzy systems. To do this, more general classes of non-parallel distributed compensation (non-PDC) control laws and non-quadratic Lyapunov functions are presented. Unlike the conventional non-quadratic approaches using only current-time normalized fuzzy weighting functions, we consider not only the current-time fuzzy weighting functions but also the l-step-past (l?0) and one-step-ahead ones when constructing the control laws and Lyapunov functions. Consequently, by introducing additional decision variables, it can be shown that the proposed conditions include the existing ones found in the literature as particular cases. Examples are given to demonstrate the effectiveness of the approaches.     

Cluster formation in a time-varying multi-agent system

We introduce time-varying parameters in a multi-agent clustering model and we derive necessary and sufficient conditions for the occurrence of clustering behavior with respect to a given cluster structure. For periodically varying parameters the clustering conditions may be formulated in a similar way as for the time-invariant model. The results require the individual weights assigned to the agents to be constant. For time-varying weights we illustrate with an example that the obtained results can no longer be applied.     

A discrete-time approach to impulse-based adaptive input shaping for motion control without residual vibration

Modifying a command or actuation signal by convolving it with a sequence of impulses is a useful technique for eliminating structural vibration in rest-to-rest motion of mechanical systems. This paper describes an adaptive discrete-time version of this approach where amplitude and timing of impulses are tuned during operation to match the system under control. Solutions giving zero residual vibration are formulated in terms of a quadratic cost function and constructed by iterative operations on measured sets of input–output data. The versatility of the approach is demonstrated by simulated test cases involving (1) amplitude optimization of impulses with fixed timings, (2) timing optimization of impulses with fixed amplitudes and (3) combined timing and amplitude optimization. The approach is model-free and directly applicable to multi-mode systems. Moreover, fast adaptation within a single rest-to-rest maneuver can be achieved.     

Time-relevant stability of 2D systems

For many 2D systems, one of the independent variables plays a distinct role in the evolution of the trajectories; since often this special independent variable is time, we call such systems ‘time-relevant’. In this paper, we introduce a stability notion for time-relevant systems described by higher-order difference equations. We give algebraic tests in terms of the location of the zeros of the determinant of a polynomial matrix describing the system. We also give an LMI characterization of time-relevant stability involving only constant matrices.