178 problems

Let the saturated linear feedback be the system defined by and, and let Proposition give sufficient conditions for its global asymptotic stability (GAS). Necessary-and-sufficient-c…

Let $X$ and $U$ be Hilbert spaces, and let $B$ be an input operator. The resolvent condition is the estimate denoted by … should be equivalent when $X$ and $U$ are Hilbert spaces.…

Periodic-solution conjecture. If all solutions are uniform-bounded and uniform ultimate-bounded, then there exists a nonzero periodic solution with period $T$, which need not be un…

Let $G$ be a discrete-time, linear time-invariant plant in negative feedback with a nonlinearity whose slope is restricted to $[0,k]$. Let $k_{AS}$ be the supremum of the values of…

Let $G$ be a stable transfer function, let $k_N$ be its Nyquist value, and let $\phi$ be a memoryless nonlinearity in $S[0,k]$. Kalman conjecture. The feedback interconnection of…

The paper studies functionally affine linear parameter-varying systems and their linear fractional transformation representations; in the discrete-time setting, the proposed transf…

High-SNR control-capacity conjecture. In this “high SNR” regime, the ratio of the mean to the standard deviation of $B$ is essentially what dictates the scaling of control capacity…

Let $m,p,n$ be positive integers with $n=mp$, let $d(m,p)$ denote the relevant enumerative degree, and let $\chi$ be the pole-placement map for the systems under consideration. Gen…

The paper considers methods for constructing closed-form strict Lyapunov functions for hybrid systems from suitable nonstrict Lyapunov functions, including systems with decay condi…

Consider a general control system and the two notions of flatness and Monge parameterization: flatness requires a flat output whose associated formulas recover the system variables…

Let $\Omega$ be the domain of a system … mathrm{d}omegawedgeomega=-left(frac{S}{2g4},mathrm{d}lambdawedgeeta+frac{T}{2g4},mathrm{d}lambdawedgeomega^1+J,omega^1wedgeetaright)wedgeom…

Consider two locally controllable gradient systems, with state spaces equipped with their underlying pseudo-Riemannian manifolds, and let a state space diffeomorphism identify thei…

Linear stability conjecture. The same result should hold for generic polyhedral patchy vector fields on $\mathbb R^n$: impulsive perturbations should generically produce a perturba…

Generic-position conjecture. The situation should be better when the patches are in “generic” position.

Consider an unstable scalar process with instability parameter $\lambda$, controlled over a channel. A controller has finite memory when its control action depends on only finitely…

Non-actuated cycle conjecture. The presence of a non-actuated cycle in the network prevents the stabilizability condition from being satisfied.

Russell–Weiss conjecture. The Hautus test is sufficient for exact controllability of the system.

Homotopy conjecture. A homotopy viewpoint—a continuous deformation between linearizing morphisms, rather than commitment to a single one—can regulate references and operating regio…

Let the control be restricted to the finite-dimensional subspace generated by Fourier modes indexed by … where $m$ is a mode index. Controllability conjecture. A control with this…

Let $H$ be the stabilizing positive semidefinite solution of the reduced discrete algebraic Riccati equation under Assumption, and let ${\mathcal V}_{\mathcal L}$ denote the struct…

Let … and suppose that $P$, $Q$, and $R$ are linear combinations of polynomials $P_1$, $Q_1$, and $R_1$ satisfying Conjecture 1, with the combinations coupled by a non-degenerate m…

Let … where $W_c(s)$ is the transfer function of a linear subsystem and the polynomial factor is linear in $k=(k_1,k_2,k_3)$. Ruled-boundary conjecture. If each of the polynomials…

Let $M_{0}$ be the halving parameter, and let $(P^{*}(M_{0}),\beta^{*}(M_{0}))$ denote the solution of the LMI parameterized by $M_{0}$. Consider the open set of values of $M_{0}$…

Policy-iteration convergence conjecture. The method converges for sufficiently large $\beta$.

Extension of the projected closed-loop ISS result. Under standard model-order-reduction assumptions, the closed-loop dynamics on the submanifold…