Raphael Sivan

Modern signals and systems

Overview of signals and systems an introduction to signals an introduction to systems difference and differential systems state description of systems expansion theory and Fourier series Fourier transforms the z- and laplace transforms applications to signal processing and digital filtering applications to communication feedback and applications to automatic control supplement reviews and SIGSYS tutorial.

A non-linear optimal control law for linear systems

In this paper a nonlinear feedback control law will be constructed for a class of linear systems, To this end a. very particular criterion functional is introduced, involving a certain S-norm of the state ||x : ||x||s. When ||x:||s = 0, singular phenomena occur which are considered in detail. It is shown that optimal arcs may end up with a singular trajectory. This problem is considered for n -dimensional linear time-dependent systems with vector control.

False cue reduction in moving flight simulators

When roll motion is simulated on a moving flight simulator, false cues are frequently perceived by the subject pilot that degrade the quality of the simulation. In order to reduce the false cues, an adaptive approach based on a real-time simulation of the subjects vestibular organs is suggested. This approach is compared both to a linear washout filter commonly used in moving base simulators and to a previous adaptive attempt to eliminate the false cues.

Maximal stability robustness for state equations

A measure for stability robustness of a linear time-invariant finite-dimensional system state equations is introduced. An upper bound for the measure is derived using the characteristic values of the system. It is shown that the set of optimal systems, namely, systems for which the stability robustness measure attains the bound, contains the normal set, which has been considered as the set of optimal robustness. >

Stability robustness of almost linear state equations

Sufficient conditions for stability robustness of finite-dimensional autonomous systems are discussed. The system comprises a stable linear nominal part and different types of unstructured norm-bounded perturbations. Quantitative sufficient conditions for stability robustness are introduced for the case in which the perturbations are almost linear, in the sense that both the size and the derivative of the perturbations are bounded. These conditions describe a tradeoff between the size of the perturbations and their distance from linearity. The arbitrary nonlinear case and a special linear case are shown to be limiting cases of the almost linear type. As an illustration, the same quantitative sufficient conditions for stability are applied to a system with slowly varying linear perturbations. >

Stability, Controllability, and Observability of the “Four State” Model for the Sarcomeric Control of Contraction

A model of the sarcomeric control of contraction at various loading conditions has to maintain three cardinal features: stability, controllability (where the output can be controlled by the input), and observability (where the output reflects the effects of all the state variables). The suggested model of the sarcomere couples calcium kinetics with cross-bridge (XB) cycling and comprises two feedback mechanisms: (i) the cooperativity, whereby the number of force-generating (strong) XBs determines calcium affinity, regulates XB recruitment, and (ii) the mechanical feedback, whereby shortening velocity determines XBs cycling rate, controls the XBs contractile efficiency. The sarcomere is described by a set of four first-order nonlinear differential equations, utilizing the Matlabs Simulink software. Small oscillatory input was imposed when the state variables trajectories reached a steady state. The linearized state-space representations of the model were calculated for various initial sarcomere lengths. The analysis of the state-space representation validates the controllability and observability of the model. The model has four poles: three at the left side of the complex plane and one integrating pole at the origin. Therefore, the system is marginally stable. The Laplace transform confirms that the state representation is minimal and is therefore observable and controllable. The extension of the model to a multi-sarcomere lattice was explored, and the effects of inhomogeneity and nonuniform activation were described.

The bounded energy optimal control for a class of distributed parameter systems

The bounded energy optimal control for one-dimensional linear stationary distributed parameter system is solved here. The criterion function is a quadratic functional of the output. Obtaining the optimal control involves the computation of the solution of a certain non-linear integral equation. The method of solving this integral equation is approximating the kernel of the integral operator by a sequence of degenerate kernels. It is shown that the sequence of approximate solutions of the approximate integral equations converges to the optimal solution; and that the sequence of approximate values of the criterion, converges to the optimal value of the criterion.

Inverse Radial Matrices and Maximal Stability Robustness

In this work properties of inverse radial matrices and their relations to generalized stability radii are discussed. A characterization of an inverse radial matrix is introduced. The connection between these matrices and the stability radii is presented. The case of equality between the complex and the real stability radii is characterized.

Identification of the intracellular control of the cardiac force-length relationship: Analysis of the hystereses in the force-length plane.

Revealing the mechanisms underlying the regulation of the cardiac muscle force-length relation is of immense importance for the understanding the normal and failing heart functions. Our model of the intracellular control of contraction includes two feedback loops: 1. The cooperativity (positive feedback) mechanisms, whereby the number of force generating cross-bridges (XBs) affects the rate of new XB recruitment. 2. The mechanical feedback, whereby the sarcomere velocity determines the time over which the XBs are at the strong state. The study aims to verify the ability of the model to explain the experimentally observed hystereses in the force-length relations (at constant activation) and to determine the role of each feedback loop. The force response to large (>4%) sarcomere length (SL) oscillation lags the length changes at low frequencies (<4Hz), leading to a counter-clock wise hysteresis. At high frequencies (>4Hz) the force precedes the SL oscillation and clockwise hysteresis appears. The model of the sarcomere, that couples calcium kinetics with XB dynamics, was built on Simulink. The force responses to SL oscillations were simulated at constant calcium concentration (activation). When the mechanical feedback is opened and only the cooperativity feedback exists, the force lags the SL. Opening the cooperativity mechanism and leaving only the mechanical feedback yields the opposite phenomenon and the force precedes the SL. The cooperativity dominates at low frequencies, when both feedbacks exist, while the mechanical feedback dominates at higher frequencies, in accordance with the experimental observations. The study emphasizes the role of each feedback.

Design of closed-loop systems with bounded transmission or bounded sensitivity

This paper considers the design, in the frequency domain, of controllers for SISO plants, so that the closed-loop system is asymptotically stable, has a sensitivity function with zeros at given points in Re (s) ⩾0, and has a transmission or a sensitivity function bounded by a given function. The design requirements are reduced to an interpolation in Re (s) ⩾0, and a necessary and sufficient condition for its solution is presented. An algorithm is given for the construction of the required controllers.