What’s decidable about linear loops?

We consider the MSO model-checking problem for simple linear loops, or equivalently discrete-time linear dynamical systems, with semialgebraic predicates (i.e., Boolean combinations of polynomial inequalities on the variables). We place no restrictions on the number of program variables, or equivalently the ambient dimension. We establish decidability of the model-checking problem provided that each semialgebraic predicate either has intrinsic dimension at most 1, or is contained within some three-dimensional subspace. We also note that lifting either of these restrictions and retaining decidability would necessarily require major breakthroughs in number theory.

Dynamic logarithmic state and control quantization for continuous-time linear systems

This paper addresses logarithmic quantizers with dynamic sensitivity design for continuous-time linear systems with a quantized feedback control law. The dynamics of state quantization and control quantization sensitivities during “zoom-in”/“zoom-out” stages are proposed. Dwell times of the dynamic sensitivities are co-designed. It is shown that with the proposed algorithm, a single-input continuous-time linear system can be stabilized by quantized feedback control via adopting sensitivity varying algorithm under certain assumptions. Also, the advantage of logarithmic quantization is sustained while achieving stability. Simulation results are provided to verify the theoretical analysis.

Stability analysis of nonlinear impulsive switched positive systems

In this paper, the global asymptotic stability (GAS) of continuous-time and discrete-time nonlinear impulsive switched positive systems (NISPS) are studied. For continuous-time and discrete-time NISPS, switching signals and impulse signals coexist. For both of these systems, using the multiple max-separable Lyapunov function method and average dwell-time (ADT) method, some sufficient conditions on GAS are given. Based on these, the GAS criteria are also given for continuous-time and discrete-time linear impulsive switched positive systems (LISPS). From our criteria, the stability of the systems can be judged directly from the characteristics of the system functions, switching signals and impulse signals of the systems. Finally, simulation examples verify the validity of the results.

Algorithmic Differentiation of the MWGS-Based Arrays for Computing the Information Matrix Sensitivity Equations within the Problem of Parameter Identification

The paper considers the problem of algorithmic differentiation of information matrix difference equations for calculating the information matrix derivatives in the information Kalman filter. The equations are presented in the form of a matrix MWGS (modified weighted Gram–Schmidt) transformation. The solution is based on the usage of special methods for the algorithmic differentiation of matrix MWGS transformation of two types: forward (MWGS-LD) and backward (MWGS-UD). The main result of the work is a new MWGS-based array algorithm for computing the information matrix sensitivity equations. The algorithm is robust to machine round-off errors due to the application of the MWGS orthogonalization procedure at each step. The obtained results are applied to solve the problem of parameter identification for state-space models of discrete-time linear stochastic systems. Numerical experiments confirm the efficiency of the proposed solution.